John.
Maybe a more generic name is not a bad thing. However, I never thought of what I do, as general cleaning. In fact I chose a company name to be specific in what I do.... Power wash stuff! I'm not ready to start cleaning windows, and polishing tile floors, and any non-power washing activity for that matter. I'm fine with deck restoration, exterior building washing, and some delivery truck washing.
This year I am venturing into gutter cleaning and repair, to keep revenues coming in for a couple extra months. I'll have to evaluate the results of that before I start offering other cleaning services. My focus has been on adding additional services that directly relate to my primary services. Obviously, here is a scenario where generic company naming works well, gutter cleaning and say, deck repair, may have nothing to do with power washing. I can often add-on some extra $$ on my deck jobs by offering minor deck repairs to go along with the refinishing. But I wouldn't place a listing under "deck repair" and upsell refinishing as an extra. Not my mission.
Everybody has different strategies, and that is one of the things that keeps this business and these websites fun. There's no set path for us to follow, no blazed trails. Many paths can lead to the same destination. Our industry is wide open for the taking. Those who are aggressive, and define their niches in the market, and excercise creativity will be rewarded by great success. At least that's my take on it.
What all this means is there is no right or wrong, it doesn't matter if everybody agrees. Just go with your gut feeling based on all the knowledge and information that you can get your hands on, and you'll make the decision that is best for you.