There are a number of different types of syncretic relationships:
Some were political, often involving foreign deities. Serapis (making an Egyptian deity who would be acceptable to Greeks), Arensnuphis-Shu, etc.
Some were one god inhabiting another. In the Amduat book, Ra comes to rest in Osiris in the middle of the night, and is recharged for the next day.
In others, the -Ra suffix is used to show the other deity taking a cosmic role. Wepwawet-Ra, Amun-Ra, etc. Sometimes the connection goes in the other direction, as in Ra-Horakhty.
Combinations with the goddess Mut showed a motherhood/creator connection. Nekhbet-Mut, Sekhmet-Mut, etc. The Crossword Hymn to Mut shows this in an extreme form.
In some cases there's a male/female fusion: Sekhmet (or Mut) and Min. Or Atum (who is both male and female) and some other deity.
In others one deity is acting as the Ba of another. Khnum is the Ba of Ra- (and Ba for a ram-aspect deitiy was a pun for the Egyptians.)
Banebdjedet (was said to be the Ba of Ra, Shu, Geb, and Osiris) and was sometimes represented as a four-headed ram.
It's a very complex subject. Erik Hornung's "Conceptions of God in ancient Egypt : the One and the Many" is one source to check.