I name them "1st Infantry, 2nd Infantry, 3rd Infantry" etc., at least when they are new.
When they get 2 stars and they start distinguishing themselves, I give them random a state, such as "1st Virginia Inf" or "1st Louisiana Inf". The state I name them usually has alot to do with who their current commander is, even if they are fictional. "John Kershaw" for instance would remind me South Carolina due to the historical Joseph Kershaw, so that brigade might be the "1st South Carolina".
When they achieve 3 stars, then they get a nickname, usually corresponding with the state, and not always historical. "Tarheels Brigade" or "Tennessee Volunteers" will work.
This helps me to distnguish them easier on the battlefield. Basically, I know who is expendable, and who is dependable.