So since I wasn't charged...when the supervisors do a background check on me, will my name show up in there database as a misdemeanor retail theft?
A criminal background check will not show this

If they do subscribe to the Retailer Database, your name and particulars will show-up when searched
And if it is on there, then I heard my record will be cleared as soon as I turn 18?(currently am 16,turning 17 next month)
The Retailer Database has NO obligation to remove your name for whatever reason