hi, Francky!
it's okay, but perhaps, I should explain the second sentence.
actually, this one simply means 'tell me your name', but in turkish, when we ask something much politely, we have a problem like this (in the translation).
however, 'may I have your name?' isn't wrong expression, methinks (and I do not understand why the requestor rejected the translation).
maybe, we can use 'may I know your name,please?'.
so, in stead of rejection, it'd be better to edit the secon sentence in the translation. what do you think, dear Francky?