It looks like some sort of Liriope, which isn't really a grass.

It will spread by rhizomes, but if you plant it in a bottomless pot, buried in the ground, you can keep it where you want it.

It likes moist fertile soil in full sun to part shade. In your zone, afternoon shade would be good.

Variegated Liriope is much slower to spread than solid. I would not be worried about it being invasive.

Great! I really didn't want to have to dig them up because I like where they are. I was also thinking since it hasn't grown much since planting back in April, that maybe I wouldn't have to worry about it spreading.

Thanks for your help!