The second person has it right. When exchanging names, Ayla rattles off her entire name, which confuses Creb. She then repeats only the first part, which Creb manages as Ay-la (sounding swallowed or gutteral or something like that), and Ayla decides that yes, she will be Ay-la for them.Later on, when Jondalar et al says her name, Ayla notes that it sounds different than the Clan says it - I imagine it to be the way most of us would pronounce it, flowing instead of "swallowed". When she meets Rydag, the half-Clan boy of the Mamutoi, the first thing she notices is that he says her name the way she used to hear it from her Clan.
The pronunciation of the name in the book is not by the Neanderthal, who communicate (according to Auel) by hand signals and primitive sounds, but is the original Cro-Magnon pronunciation of her name, a very important fact in the book as it is the only knowledge Ayla possesses about where she comes from, and the only evidence she has of her mother.
No, Creb didn't get it right. Ayla's real name is much longer, and in the book Creb is struggling to reproduce the multi-syllable word the little girl uses as her name, but he only gets as far as to Ay-la, two syllables, which is all his Neanderthal brain could handle. They weren't using language the way Cro Magnons did. I would really like to know what Ayla's real name is. Maybe Jean M Auel will let us know in the final book.
Later on, when Jondalar et al says her name, Ayla notes that it sounds different than the Clan says it - I imagine it to be the way most of us would pronounce it, flowing instead of "swallowed". When she meets Rydag, the half-Clan boy of the Mamutoi, the first thing she notices is that he says her name the way she used to hear it from her Clan.