It's actually a bit of a inside joke - one of the co-founders, Paul Graham, is a big fan of the programming language Lisp, which was invented by John McCarthy. In Lisp, there's a function called "Y combinator" (or "Y function") which is used to define recursive functions.
So when they were choosing a name for their startup accelerator program, they decided to name it after the Y combinator function as a tribute to Lisp.