Claire seems quite popular on the board, and I know one 6 y.o.
Clare, and of the three names you've listed here it's the most common (#98 or so on the SSA's list)...BUT...Elise and
Julianna are trendier, if less common, and imo lack the strength and timeless quality of
Claire.
sa
PS: my rationale for
Elise and
Julianna being trendier is as follows-
Elise sounds like the elegant French alternative to the insanely popular
Ella and
Alyssa, as well as a light version of favourite
Elizabeth and a subtle way of honouring a
Lisa. I've heard this one A LOT around here (i.e. Vancouver, BC). When I first heard it I rather uncharitably wondered if the parents (not you, the specific parents of that young lady) were subconsciously attracted to the name because it's just a phoneme away from elite.
Julianna-
Anna is insanely popular (though I love
Anne and we're considering that one), and as a suffix it's even more insanely popular- Julian(n)a, Lil(l)iana, Adrian(n)a,
Viviana,
Gianna, Lian(n)a, Brian(n)a, Tian(n)a...the long and sultry feminine names ending in -ana and -ella are so popular it's not funny!