I sometimes get ideas like this, and I think it's very fun, especially if you feel that everything makes sense and sounds good.
A while ago I invented my own letters, and I named the language "Teniorella" (Eternal Brook), which is a combination of the words "tenia" (eternal) and "ella" (brook).
This is because the letters have a pretty slender look, and they remind a lot of common script.
I also have a second name for the language, "Lumilauro" (Blue Fire), which is a compound of "lumio" (blue) and "lauro" (fire, flame) since I wrote the first characters using a blue fountain pen.
I'm pretty satisfied with these words for now, although I'll probably change them sooner or later. XD
Anyway, did you ever do this?
It's very fun if you really get on with it, it simply is creatively entertaining.