I think you could have done more to recover them when they first where stolen, but now that so much time has passed, I think it will be very difficult to get them back... I had the same problem as you, a friend from school took my accounts and years later, when I came back to play Neopets, it was too late for ask them to TNT xD
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How long have you not had access to the account? I have a few accounts similar to your issue, and they were stolen over four years ago.
TNT told me I can't get them back back because they haven't been accessed in over two years.
If this is the case for you as well, especially if you don't have password and birthday (I had a list of all prior birthdays), then they definitely won't return the account to you.
My only suggestion is to either let the account go, or wait around until someone comes along who can hack accounts for a $$$ amount.
There aren't very many people willing to hack accounts, and even more so, most of the ones who could no longer can (but working on it) or are off doing better things.
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I would suggest getting a new account to put your pets on. Maybe get a couple shells and build them up to look like mini mains.
As for your other question, it depends on what you're doing with the pet. Names aren't a huge factor, but if you plan on visiting the PC with a high end VWN UC pet, people will take notice.
If you're just getting your pet(s) and keeping them on your account and avoiding the boards, you shouldn't have an issue.
Take a look at the Neopet Guides section. There's a lot of answers there for securing pets & such
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