So I love the nickname [name_u]Kit[/name_u] for a boy or a girl, but I don’t like [name_m]Christopher[/name_m] or [name_f]Katherine[/name_f] and I don’t much care for [name_m]Charles[/name_m], either. What are some other names that could be shortened to [name_u]Kit[/name_u]? Is [name_m]Clarence[/name_m] too much of a stretch?
[name_m]Atticus[/name_m] nn [name_u]Kit[/name_u] is one I see a lot. Also [name_m]Beckett[/name_m], [name_m]Kester[/name_m], [name_f]Kristen[/name_f], or [name_m]Kingston[/name_m]
I’d say [name_m]Kenneth[/name_m] and [name_f]Kathleen[/name_f].
I wouldn’t expect a [name_u]Kit[/name_u] to be named [name_m]Clarence[/name_m], but it’s not that it wouldn’t work.
Would you consider any [name_m]Christopher[/name_m]/[name_f]Catherine[/name_f] variations like [name_m]Christophe[/name_m], [name_f]Catriona[/name_f], [name_f]Caterina[/name_f], [name_f]Katrin[/name_f] etc?
You could also use initials. For example, [name_f]Kaia[/name_f] [name_f]Tallulah[/name_f] nicknamed [name_u]Kit[/name_u]. Or combine the first and the middle name, like [name_f]Kaia[/name_f] [name_f]Alouette[/name_f] nicknamed [name_u]Kit[/name_u].
[name_u]Kieran[/name_u], [name_m]Corentin[/name_m], [name_u]Constantine[/name_u], [name_m]Clement[/name_m], [name_u]Nikita[/name_u], [name_m]Whittaker[/name_m]
[name_f]Callista[/name_f], [name_f]Clementine[/name_f], [name_f]Cosette[/name_f]
I like [name_u]Kit[/name_u] for a boy or girl too.
Here are a few that I don’t think have been mentioned yet:
Girls-
[name_f]Katia[/name_f]
Okay, that’s all I got. I love it though. [name_f]Kathleen[/name_f] is also sweet.
Boys-
[name_f]Cricket[/name_f]
[name_m]Crispin[/name_m]
I think that [name_m]Clarence[/name_m] could work, if you like that.
[name_f]Hope[/name_f] this helps. 
[name_f]Kaitlyn[/name_f]
[name_f]Katrina[/name_f] / [name_f]Katerina[/name_f]
[name_f]Kalista[/name_f] / [name_f]Callista[/name_f]
[name_f]Kristen[/name_f] / [name_f]Kirsten[/name_f]
[name_f]Katia[/name_f]
[name_f]Kristina[/name_f] / [name_f]Krista[/name_f] / [name_f]Kristiana[/name_f]
[name_f]Constance[/name_f]
[name_f]Kourtney[/name_f]
[name_f]Crystal[/name_f]
[name_u]Constantine[/name_u]
[name_u]Kristian[/name_u] / [name_m]Christian[/name_m]
[name_m]Kurtis[/name_m]
I think [name_m]Clarence[/name_m] ‘[name_u]Kit[/name_u]’ could work.
Some others I like as full names with [name_u]Kit[/name_u] include:
[name_m]Killian[/name_m]
[name_u]Curtis[/name_u]/[name_m]Kurtis[/name_m]
[name_m]Atticus[/name_m]
[name_m]Caspian[/name_m]
[name_m]Casper[/name_m]
[name_f]Catalina[/name_f]
[name_f]Klara[/name_f]
[name_f]Kalista[/name_f]
[name_f]Cadence[/name_f]/[name_f]Kadence[/name_f]
[name_f]Constance[/name_f]
Bit of a late response, but I have considered [name_u]Kit[/name_u] as a nn for [name_f]Victoria[/name_f] before
I’ve used [name_m]Atticus[/name_m] for [name_u]Kit[/name_u] a couple times, plus have considered [name_u]Kieran[/name_u] and [name_m]Cassian[/name_m], though I eventually decided that the latter would suit [name_u]Cass[/name_u] better. [name_m]Crispin[/name_m] is equally good with [name_u]Cris[/name_u] and [name_u]Kit[/name_u], and [name_m]Chester[/name_m] can be [name_m]Chet[/name_m] or [name_u]Kit[/name_u] as well. Might use [name_u]Cal[/name_u] for a [name_m]Calixto[/name_m] or [name_f]Callisto[/name_f] instead, though [name_u]Kit[/name_u] suits them both. [name_m]Costello[/name_m]?
If you’re not willing to consider any of the [name_f]Katherine[/name_f]/[name_f]Catherine[/name_f] family for [name_u]Kit[/name_u], you could also try the ones mostly connected with [name_m]Christopher[/name_m]: [name_f]Christine[/name_f], [name_f]Christina[/name_f], etc. [name_f]Katya[/name_f] is technically a diminutive already (Russian, I think, like [name_m]Viktor[/name_m] and [name_m]Vitya[/name_m]), probably of a [name_f]Katherine[/name_f] variant, but you could use it. Wouldn’t recommend it for [name_f]Cosette[/name_f], personally, since I see it as a nickname already, and I’m not the type to nickname a [name_m]Jim[/name_m] [name_m]Jimmy[/name_m].
Could use initials like others have suggested. K. I. T. or K. T. or something.