Enlli is from Ynys Enlli, which is a small island off the NW Welsh coast - the name basically meaning 'island in the currents'. I love it to bits, because I have connections with the island. But it wouldn't be an easy name to have, anywhere other than Wales.
Was it Gwyndaf?
And yes, we do have the nicknames thing too. I compiled a chart of Welsh names from the recent data, and there are quite a few nns in there as full names -
Cadi,
Mali, Nel, Beca, Llio - and I was quite surprised to find 3 Myfis! (for
Myfanwy, which is very dated and hardly ever used now)