I did try to get Raffy to choose his name when we first got him as we had a shortlist of three and couldn't decide. So I thought I'd let Raffy decide by calling out each name and seeing which one he responded to. It was hopeless ha ha., He perked up and responded to all of them exactly the same - it was tone of voice he was responding to mainly.
Hamsters do sometimes look at screens though. I have a photo of Newt looking at a picture of himself on my computer screen. So maybe they could choose from a tablet!