When you say "odd" do you mean "wrong" and "not appealing"? Or may "quest it" have some chance to sound "archaic", "adventurous" or "intriguing"?
It does sound odd because, exactly as SoothingDave said, we normally "quest for" or "quest after" something. So it would more naturally be "Quest after it" although that sounds like you're saying "The word QUEST comes after the word IT".
Between "wrong, not appealing, archaic, adventurous, intriguing", I would have to choose "wrong", I'm afraid.
Having said that, the titles of companies and groups are frequently ungrammatical (Toys R Us, for example, would be very odd in normal English even if they had spelt "Are" correctly).
The simple answer is that you can call your group anything you like - it just depends on whether you want people to understand what the group is about simply from reading the name. If not, you can make it as unclear or intriguing as you like.