Most people do not know what ADC, Animal Damage Control, Wildlife Control, Predator Control, etc. is. What you will want to do after choosing and registering your name is to focus on name branding, so people know what you do. There are lots of good examples of name branding such as McDonalds, Orkin, and NAPA where the name doesn't have any meaning with what the company is offering, but do to name branding everyone automatically knows.
The bigger issue you have with choosing a name, is to make sure that you aren't using one that is state (in the state you want to offer services in) or federally trademarked.
Several examples of federally trademarked names include "Critter Control", "Wildlife Solutions", and "Bats, Birds." In order to legally use these in a company name, you'd need to have permission from the owner. For instance, I own the federal trademark on "Bats, Birds" so anyone using these terms could be in violation if they started after my trademark was registered and didn't get my permission for use. This is where having an attorney research your name before registering it can pay off before you go through all the hassle only to get a cease and desist letter from the trademark owner's attorney.