Yeah, Crono's mum is actually called 'Gina'. I was really surprised the first time I played the game in Japanese because I was expecting 'Crono no okaasan' or something and it was suddenly like; "Whoa! She has a NAME!?"
Sadly the Japanese version sheds no light on Crono or Glenn's surnames, I guess because they're not important...Unless 'Glenn' is Glenn's second name, which isn't impossible, since they call him 'Sir Glenn' and often young men of educated or noble backgrounds in the past (or even today in England in some places) call each other by their surname (lots of my Brother's friends call him 'Holden' rather than 'Joe'.) ...Of course, if Glenn's second name is 'Glenn'...what would his first name be!?
Ayla is unlikely to have a second name, since the system of having them only began to emerge, in most civilisations, with the invention of census. The population Ayla's race is simply too small for there to be a need for second names. We can probably assume, there is no writing yet in Ayla's time, so no means to record data, and thus there will be no census taken of the population or anything like that. It is likely that Ayla was given the title 'chief' as leader of the tribe, as acknowledgement as her place as leader. I don't think she chose the title herself.
Crono's second name remains a mystery though.