The name Y Combinator is a metaphor: startup growth is "recursive" in a sense and Y Combinator builds such "recursive" companies out of a non-recursive input (the founders themselves)

Also Paul Graham is a Lisp nerd

(Note, I tried to find an authoritative source on how the name was chosen - the only thing I found was https://paulgraham.com/ycstart.html that lists when, but not how the name came to be; but I think this metaphor is somewhat obvious)