I'd do it anyway. DD is A.nnabelle, and we call her B.elley or B.elbo - I don't even know why! DD has now started calling herself B.elbo, it's probably the easiest for a two year old to say. Anyone who is close to us, including daycare, will call her either of those three names.
MIL used to try calling her Anna, Annie, Belle and Bella. We just told her that's not her name and in the end she gave up - no one else used those names so why should she!
If in future DD decides to go by one of those names or something different, that's fine. It's up to her, and because it's her I won't mind what her name is. I think it's easy enough to get over dislike of a name when it's your own child requesting it.
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