The Rack. Simple but catchy, as in "hey see you at the Rack tonight" or "happy hour at the Rack?" And the next locations could be named similiarly, The Cue, The Table.
Lucky Rack, Lucky Break (I think your other one is named Lucky 9 right?)
The Last Drop. More for a bar, but would work for a pool hall. Reminds me of your local, down the street kind of place.
And for some strange reason I also like The Square Rack. Just seems to stick in my head because it's odd.
Best of luck and it's really great to hear about a pool hall opening and obviously your existing place is successful. :thumbup2: