We should consider our audience and allies when choosing a name. We need a name that appeals to our core base while not scaring away untapped members and alliances.
The Bill of Rights Coalition is great because it encompasses interests of all our major audiences. Our allies on the left love the 1st and 4th amendment. Our allies in the Tea Party love the 2nd and 10th amendment. We will fight for them all, and we can draw support from both sides.
Also consider that this will be a multi-state PAC, so the Coaliton suffix is fitting.