Real name or is my nick name ok?.?

[Javelina]

Using Vito instead of Vittorio is just fine for Twitter and Facebook. For PayPal it is a little more important to be consistent with your banking, but you can change it on PayPal if you need to. You should leave Twitter and Facebook as the name you've established, don't change it now.

For work, that's fine if you are known as Vito. However, it is important that you use the same name on bank account and your social security card (and passport, if you have one), when you fill out applications for jobs, or sign contracts or whatever arrangements that people in the motion picture industry make. There's an actor's union, and a writer's union, so if you're in one of them, use the name that is on your bank account and social security card. Be very consistent about this! If your bank and social security card say Vito, use that. If they say "Vittorio", then use "Vittorio". For all other things, you can keep using Vito.

EDIT: If you use LinkedIn, I'd suggest using your real name, unless doing so will mean people can't find you when they look you up in search!