What puts me off
Diana is the inevitable use of
Di as a nn. And of course the association with the former owner!
Are you the kind of person who would name a child after a celebrity? If you are not, your friends will know; and if other people suspect that you have, doesn't that say more about them than about you?
Of course, you could consider using it as a mn, or substituting
Diane or, preferably,
Dinah.
By chance, I gave my first daughter a name associated (by some!) with royalty - not British. And a friend whom I'd always thought was pretty sensible assumed it was "because of" this princesssy person. I stared at her blankly and said "Oh, no, I've never met her" which led to a swift change of topic!