I like
Hilary (one l only, please) well enough and the nn Hilly which is kind of cute. The problem is that it reminds me of hilarious (which it means, of course). One of my dds had a friend named
Hilary. Her surname also began with the letter H and I loved the alliteration of it.
Perhaps it hasn't been more common due to
Hillary Clinton. She's been on the national scene for some time. Maybe the name reminds people of hilarious. I think it's a name worth using.