I got bullied in the 80's for my unusual name.
My DC have unusual names and say they have never been bullied or laughed at for their names.
We live in a part of the country where there are lots of Eastern Europeans, Portuguese and folk from Madeira and so the names of the kids mates are really diverse.
I do think we have left the bad old days behind and a persons name is just that with minimal connotations.
Obvs there will still be the old class divide between the British, but in general I don't think kids names lead to bullying in the way the used to. And honestly hurrah for that!