I think if we're talking about Habbo names here then you should be allowed your Habbo name no matter what.
In my honest opinion, as the user has to achieve VIP before getting their name changed and achieving VIP is not easy and it's going to be getting a lot harder as management are tightening VIP restrictions as too much is given out, I don't like using individual examples but here I am going to, Saurav, banned almost 2 months ago rejoined on a brand new account (this in itself is punishment), he has to establish this account and something I found with Saurav, is he really didn't like the restrictions on the newer accounts (which is natural if you're used to the full features) and we saw this in feedback :P So in my opinion there the ban worked, Saurav then participated in the Habbox Election in which he put a lot of effort into, he earned his VIP well therefore in my opinion he deserved his name back.
It's the same with Blinger really, although he came back on an older account he found he still had to re-establish himself and get used to having less features than he's used to.
At the end of the day my view is to be lenient on banned members as it's so easy to permanently ban someone and then they don't come back to the forum. Just because they can be a nuisance and get themselves permed doesn't mean we want them to leave, so we shouldn't really push them away and I think helping banned members reestablish themselves is a good thing.

