I was cleaning my room the other day (moms -_-) when I came across an old conlang of mine.  The reason why I abandoned it in the first place was quite stupid -- I didn't know what to name it.  So... you get the idea.  Here are some details that you might use to give you ideas as to what to name it:

-It has two alphabets - one rather close to Arabic (so close that it could be considered a "dialect" of the script) and one that is Latin.  It isn't like Japanese where there are different situations in which to use a different alphabet, it was just that two alphabets were proposed by its speakers to be the alphabet: Arabic because it took up less room, Latin because the Arabic version was quite complicated.
-Its sound is based on Icelandic
-It's used especially for written documents, even if you do not even know the language (to them, it was like heiroglyphics where all you had to do was look at it and know its meaning, it worked kind of like "Okay, this word spelled ser means to be even though I haven't a clue what Spanish even is")
-It was the language used prior to the last ice age, when large civilizations were wiped out, killing major languages such as this one (and it's pretty awkward having a conlang with a story like that - I'm a Creationist)