Can I use the name Kathy (Kathleen) which I was working under for 32 yrs for my CPP?

If Kathy is a nickname among coworkers, than there's no problem in using it. If you permanently want to change your name from Kathleen to Kathy...then there's a lot of paperwork lol. Nicknames are harmless unless you have the intention of changing it from a nickname to just your name...:)