Picasa accounts are not separate from Google accounts.
So the first thing to try is going in to Picasa when you are already signed in to gmail.
If you have no albums (or not the right ones), then you must have used Picasa with a different Google account. What you need to remember is the email address that you used to create that Google account. It may be a gmail address - or it may be a different email address. If it was long time ago that you did this, then it did not even have to be an active email addresss - just a string of text that looked like one.
I'm not sure if Picasa has a "forgot your account name" option. Do you have any links to Picasa-albums that you want to find the account name for? If not, then you will simply have to remember without any help from Google.