I don't mind it at all, not my favourite but I don't hate it. In the end, it only really matters if you love it. As for DP's parents, they already had their chance to name a DC, they don't get to decide on names for yours. Most grandparents grow to love the name of a grandchild, even if they previously didn't like it, because they associate it with them.
As for nicknames, I know one Dianna (that spelling) and not only has she never shortened her name, but it has never occurred to me to do so either. I think it's one of those names where people don't automatically reach for a shortening or a nickname.
The only thing I will say is, in the accent where I grew up, Diana sometimes sounds like Dinah, or DY-uh-nuh, with the emphasis on the first syllable rather than the second. It's always worth taking into account what local accents would do to a name you love. (eg, where I'm originally from, Amelia is mostly pronounced Amil-ya, and I've seen several complaints in this board about people local to them pronouncing it that way!).