Your ideas of calling your company either Amec Insurance Agency or Apex Insurance Prime Insurance are good choices. Some other ideas to possibly consider includes:
1. Include the word "Georgia" in the name would be a good idea.
Georgia Insurance Group
Georgia Network Insurance
Could you then take out "Georgia" and use other directional terms similar such as"
Look also at other features of the state to incorporate in the name. For example:
State Flower- Cherokee Rose
State Bird- Brown thrasher
State Creed- Georgian's Creed
State Gem- Quartz
State Mineral- Staurolite
State Tree- Southern Live Oak