Search:

Ася? ( "Тётя Ася":D :D :D )
Hmm... imagine this:
- My name is Ася. Тётя Ася...

BTW "Прозвища". "Ча-ща пиши через а". :)

I don't think "Pravit" is a kind of name which makes good nicknames.
Правитик sounds stupid, and Правичок resembles "Новичок".

"Снежок"! :D :D ha-ha-ha, like a doggy name!
May be he'll want to be Весик, Севрик, Снейпон (rather vulgar and colloquial).
If it is HER (may be lover?) who calls HIM, let it be Весик. Sounds...

Юрец...
what else? :P

Yurochka is too caressing name. Or it may be a little derogatory, as looking from highly above. I think only the closest friends and relatives may use it freely.
Yuri Mikhailovich Kirov is OK.