THE NAMES OF THE PAIR
Next to their pictures on the papyrus, the divinities' names (or epithets?) are written in Medw Neter, the "Words of God," i.e. hieroglyphs by their designation in the language of Ancient Egypt. The god towards the left is called "Pure/Special/Holy Ba." The other one, towards the right, is called "Perfect Ba Shut."
In 1912 the British Museum published Sir Ernest Alfred Thompson Wallis Budge's book, all on this subject, titled The Greenfield Papyrus in the British Museum: The Funerary Papyrus of Princess Nesitanebtȧshru, Daughter of Painetchem II and Nesi-Khensu, and Priestess of Amen-Rā at Thebes, About B.C. 970. In it Budge supplies a detailed description of every "collotype facsimile" that was made into image-plates from the contents of the papyrus.1
The image you're asking about is numbered "Sheet 87" and shows up on "Plate CVI," which is displayed on p. 358 and supplied with a description and interpretation on pp. 79-80:
On the right of Shu2 stands a ram-headed god, with his
hands raised, who is described as the "perfect soul Shut (?)"...
Budge then indicates that this is a translation of the line of text directly above this character's head, beneath Nut's mouth.
Budge most commonly translates ba as "soul" (although Ancient Egyptian psychological anthropology is about seven times more complex than the English word "soul" might suggest, but he evidently does it in order to provide a more familiar term for his readers). The question-mark applied to the word Shut implies that he is unaware of what it signifies. Perhaps it is the name of this "perfect soul/ba" (and might be a word related to Shu?).
In front of Shu3 stands a similar ram-headed god, who is
as his label indicates, "Special Ba" or rather, as Budge puts it, "Holy Soul".
See the column of text directly behind this god, in front of Nut's shins. His name appears at the top of the column, which is actually the end of this phrase (which has been written from bottom to top).
(Here's a detail of the relevant portion of the image, for easier reference.)
In between Shu and Special-Ba is another piece of text which says "Rā Sets in the Land of Life." Rā is, however, absent from the image, as Budge notes at the end of his breakdown.
Next to the arm of the goddess, directly behind Perfect-Ba-Shut, is a text column which reads "The Sky, the Support of Rā: Nut, the Mother of the Neteru" (the Neteru being the Gods).
Some papyri and other documents represent the sun sailing over
the back of Nut in two boats, one being the boat of the morning sun,
and the other the boat of the evening sun, and elsewhere we see the
god Shu holding up the boat of the sun, with the solar disk on the
horizon. On the left, a little above the hips of the goddess, facing
the god of Eternity, is another ram-headed god, who kneels with his
hands raised in adoration of the goddess.
This ram-headed god's name is, according to the three-line block of text directly in front of him, the "Ba Which Embraces All Things." The "God of Eternity," pictured just in front of Nut's head, is called Ḥeḥ, and, more precisely, he represents the figure of a million (or a plurality of millions of) years [= the literal meaning of his name] rather than eternity.
In 1920, An Egyptian Hieropglyphic Dictionary, another book by Budge, was published.4 I've looked through it for a straight transliteration, rather than a translation, of the names he provides for the two ram-headed deities in question from The Greenfield Papyrus. Nothing I've found comes close to anything like "Perfect Ba Shut," but there are two different names which he says both mean "Holy Soul," both of which appear on p. 199 of the dictionary. The first of them, Ba-sheps, he says is "a title of Osiris," while the second one, Ba-tcheser, is, he explains, "a form of Osiris."
Neither of these, however, seems to refer to the "Holy Ba" in our scene. The hieroglyphs for ba are the only portions of the words which match. Incidentally the (completely theriomorphic) ram standing directly in front of Nut (by her arm, below Ḥeḥ) is labelled Ba-shep (still in hieroglyphs which fail to correspond to the characters we're looking at). The difference between this and Ba-sheps seems to give Budge pause about what this word means but his guess is that it might also mean "Holy Soul."
Additionally, on Sheet 86 of the papyrus (the sheet immediately preceding ours), Princess Nesitanebtȧshru appears kneeling before and saluting yet another ram-headed god, this one wielding a sceptre, wearing the Atef crown, and named Ba-ṭesher. The dissimilarity between this name and Ba-tcheser is very subtle but, going by Budge, it makes all the difference, since he translates it as the "Red Ram", so apparently not the same as the aforementioned "Holy-Soul form of Osiris", unless, i.e. we are to understand "Holy Soul" and "Red Ram" as puns for each other, or as otherwise-associated concepts.
Budge does not supply an explanation for who or what Special-Ba and Perfect-Ba-Shut are supposed to be beyond "ram-headed gods", but as it happens, in Ancient Egyptian the word ba also means "ram" or "sheep" (see p. 200 of Budge's dictionary), which would explain why there are so many rams and ram-headed men depicted all over the Greenfield Papyrus with names that have to do with the ba-soul (and considering also that this is essentially a comic-book illustrating Nesitanebtȧshru's afterlife sojourn).
Wind was known as Ba-en-Shu, the "Soul of Shu" (see the afore-cited p. 200 again). Perhaps Special-Ba and Perfect-Ba-Shut are projections of Shu. Shmoop, however, in its short article on this image, entitled "Shu Gets Some Help," has a different explanation for this:
What happens when Shu gets too tired to hold Nut up? He gets help from
the Heh (eternity) spirits, so they hold him up!
This interpretation of what these figures represent is perhaps not unreasonable. As mentioned above, Ḥeḥ is the man appearing as the fourth figure from the right in the topmost row of your image. Directly below him, in the middle row, is the ram named Ba-shep. Directly across from him (and facing him), past Nut's back, is the ram-headed man named Ba-Which-Embraces-All-Things. Beyond this, however, it is not at all obvious to me how Shu's companions here are connected to Ḥeḥ.
Similar compositions of these figures occur with some variations in other funerary iconography from the period. On the coffin of Tanakhtnettahat, for instance, Shu is accompanied, instead, by a pair of ram-headed birds instead of his more humanoid associates. These ram-headed versions of the birds are, however, always each equipped with a pair of human arms.
- An example of this, from a different piece of artwork, is shown below.
In her book Egyptian Iconography on Syro-Palestinian Cylinder Seals of the Middle Bronze Age (on p. 191), Beatrice Teissier5 says that in the New Kingdom, which ended just before the dynastic era presently concerning us, "Amun-Re and Re-Atum... were represented as ram-headed birds."
- In his 1904 book The Gods of the Egyptians, or Studies in Egyptian Mythology, Budge illustrates a reconstruction of such a scene, in which Shu's companions are fully avian birds (on an insert sheet between pp. 96 & 97).6
This scene has morning and evening Rā sailing along Nut's legs and arms in the boat(s) described in an earlier quote above from The Greenfield Papyrus. Shmoop identifies the two birds here as hawks representing Horus the Elder and Horus the Younger.
- A coffin at the Egypt Centre Museum of Antiquities in Swansea has a third variation with the two ram-headed companions themselves attended by a pair of part-bird figures.
Reconstruction of a fairly grungy original
- In a fourth alternative, Shu's sidekicks are a pair of what look like ba-souls, which typically are represented as human-headed birds and, in similarity to the ram-headed birds, they each have a pair of human arms too.
(Notice how Nesitanebtȧshru's ba appears in this part-bird form twice in the scene from your Question, in the middle and bottom rows to the right of the image.)
- Fifthly and finally, on the coffin of Nespawershefyt, the two human-headed (and bearded), avian ba figures appear together with Shu in addition to the two ram-headed men, making for a whole lot of fairly inconclusive evidence regarding whether the ram-headed men or ram-headed birds are supposed to signify the same thing as the human-headed birds whenever each of these pairs appears without any other pair accompanying Shu.
On another part of this coffin Shu is accompanied only by a pair of the human-headed birds.
There is one other interpretation in circulation which appears to be relatively popular. The website GodElectric.org, as well as Rolf Werner Friedrich Gross and Ottar Vendel, all say that the pair of ram-headed men is the god Khnum appearing in duplicate. This is understandable considering that although there are several ram-headed Egyptian gods, the breed of ram appearing either completely theriomorphically or as the head of numerous deities in these Dynasty-XXI artifacts looks most like the Khnum ram. However, if Budge is to be believed, they seem to tend rather towards being hypostases of Asar (Osiris).
Moustafa Gadalla7 makes these remarks in his book Egyptian Divinities: The All Who Are The One:
Khnum represents the embodiment of the creative force of Re ... Khnum
is depicted in some context as a ram-headed bird. This bird represents
the Ba of Ra [Re]—The All encompassing Ba—The Divine Soul.
1. Budge, E.A.W. 1912. The Greenfield Papyrus in the British Museum. The British Museum, London.
2. What Budge really means here is, rather: To the right of the printed image away from Shu (i.e. the reader's right), which is actually = Shu's left-hand side.
3. Now to Shu's actual right-hand side, but to the reader's left.
4. Budge, E.A.W. 1920. An Egyptian Hieroglyphic Dictionary, With an Index of English Words, King List and Geographical List with Indexes, List of Hieroglyphic Characters, Coptic and Semitic Alphabets, Etc. Volume 1. John Murray, London.
5. Teissier, B. 1996. Egyptian Iconography on Syro-Palestinian Cylinder Seals of the Middle Bronze Age. University Press; Göttingen: Vandehoeck & Ruprecht, Fribourg, Switzerland.
6. Budge, E.A.W. 1904. The Gods of the Egyptians, or Studies in Egyptian Mythology. Methuen & Co., London.
7. Gadalla, M. 2017. Egyptian Divinities: The All Who Are The One. Tehuti Research Foundation, Greensboro, NC.