What name for my bookkeeping service?

Why not have them both then. Such as yourname accounting and bookkeeping services..

How about "Book 'em, Danno"?

OK, serious answer.  What I understand you to be saying is that you're considering using "Accounting Services" in your business name because of what you might offer somewhere down the road.  If so, IMO, that's deliberately misleading.  Call it what it is now, "Bookkeeping Services,"and change the name if and when you broaden your range of services offered.

I couldn't call my car shop "Chuck's Buick and Maserati Dealership" just because I'd like to offer Maseratis some day.

Your actual business name should be short and easy to remember. Services provided can be listed below the business name and changed as your services change.

How about the name Mike's ABCs,and under that list: Accounting, Bookeeping, and Consulting on financial matters.

"Bubba the Book Cooker"

Don't use "accounting" in your name if you don't offer accounting services.

If you use "accounting" in your name but don't offer accounting services, the Acme Payday Loan Company and Pawn Shop will call and ask for an audit.

If the Acme Payday Loan Company and Pawn Shop calls and asks for an audit and you can't provide that service, their CFO, Lev, will get angry.

If Lev gets angry, he will instruct Guido to pay you a visit.

If Guido pays you a visit, you'll wake up in the ER with three missing front teeth and a split lip.

If you have three missing front teeth and a split lip, all your "s's" will sound like "th's"

If all your "s's" sound like "th's", you'll be offering bookkeeping thervitheth rather than bookkeeping services.

Don't name your company PMETH Bookkeeping and Accounting Thervitheth.  Leave "accounting" out of the name.

Guido and Bubba's Consulting Servive