Commas and nicknames

Placing commas on either side of the nickname marks it clearly as a non-restrictive appositive. In short, it's clear that "darling" is a re-statement of "Rose" which does not limit or identify Rose in any further way.

Omitting the first comma works, but it might tie the name and the nickname together, as if to suggest that "Rose" is really "Rose darling" in the speaker's mind. I suppose we could also envision a typographical error in which Rose Darling is really the person named in what would then look like an expletive of direct address.

Omitting the second comma creates a dicier situation, I think.

I think using both commas is the safest choice, although cases could be made for other punctuation. Such variations might be useful in, say, a dramatic script, where punctuation can direct an actor's phrasing.