It's obvious why 𐌂𐌀𐌕𐌌𐌉𐌕𐌄 is catamite, but not how the Etruscans got it from "Gadymedes".
Is it just "We know they're the same character / name, but we dunno how the Etruscans got there"?
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It's been a while since I looked at Etruscan, but two things that stuck out was that the language doesn't seem to get along well with voiced stops (like [g] and [d]), and also that they tended to reduce the number of vowels & syllables in their words. A quick review of the Wikipedia list of Etruscan mythological figures shows that this is a regular occurrence:
Achmemrun < Gk Agamemnon
Aitas < Gk Hades
Catmite < Gk Gadymedes :: of note, Latin borrowed this name as Catamitus and also Ganymedes from Greek
Metus < Gk Medusa
Rathmtr < Gk Rhadamanthys
Satre < Lat Saturnus