Business names need to be remembered, easily associated with the service/product line.
Easy to say as well, if you're answering the phone, by the end of the day you'll get tired of saying Merrimack Valley Residential I'm sure.
Shorter fits better on business cards, centers on letterhead, fits on stamps to endorse checks and costs less for type setting too.
How about signs, cost per letter, big names, small letter size can't read it as well far away.
How will you brand your business, got a slogan, a motto, a saying that identifies you? Some like that, so does it flow with the name?
It also needs to say what you do.
That's why you'll see someone's name and then Real Estate or Realty (you can't use Realty unless you're a Realtor BTW). Trump Inc. or just Trump! Brennan LLC works too.
I don't care for AAA unless you're a car club or a car repair shop. The phone book use to be important to some, being first on any list has advanatges.
Can the name tie into a logo? Company colors, how's it look in royal blue and light grey, red and white, yellow and black....?
One word is usually better to tie things together, while it could be
BRENNAN PROPERTIES LLC, dba "BRENNAN"
How are contracts going to be printed up, filled in, you'll have a ton of paper work and signatures, you can shorten things with the DBA and LLC.
I get a laugh out of very small companies with implications of being some mega structure, thanks for not going there like Brennan American Enterprises.... :)
I suggest you keep it simple, say what it is, and make it easy to say and write!
From what you have, I'd vote for Brennan REI (or Real Estate or Properties) :)