Zara my first hamster was called Hammy too
He was actually a boyfriend's hamster before we moved in together, so already had a name. I really fell in love with that hamster and was heartbroken when he died in surgery. (The boyfriend is long forgotten!)
Our first hamster in recent years was named by OH little boy who liked Charlie and Lola - hence Charlie. Initially he wanted to call the hamster the same as his but I said that could be a bit confusing so he chose Charlie.
After that we had a family name choosing session each time with shortlists. And usually managed to find something we all felt was right. The next one was Newt (after Newt Scamander). OH and I weren't sure about it so he was actually Newton, shortened to Newt - but ended up being called Newtie Pootie!
We then had a robo and unanimously chose Nugget after looking up names. He really was a little nugget and it suited him.
Then I adopted Moo (Syrian) a black and white hamster who was already called Moo and we liked it so kept the name.
Then came Pickle - again we all unanimously liked that (hard to find things OH liked).
Raffy was chosen by me alone. I found that quite scary! Choosing the name myself. Nobody else was that interested in the naming game any more. He was called Sprite when he arrived (which described his nature well) but I wanted to choose a name for him that felt right for us and suited him. Took me a while to come up with Raffy (short for Raphael) but he answered to it