Felicity, it's lovely. It's a name that never occurred to me when pregnant with either of my dd's but if it was I'm sure it would have been on my list somewhere.
It's a difficult name to shorten, I remember years and years ago on Neighbours, there was a Felicity (sure it was Holly Valance who played her) who's name was shortened to 'Flick' but I'm not sure about that myself. Liss/Fliss sound nice though.