For many businesses, a generic name is not going to be available within budget, or would not have enough impact.
Other alterrnatives include, cheaper dictionary words (how about confused.com?) Personally I think this approach is like trying to fit a square peg in a round hole, it might work but chances are it's just a waste of effort/money.
For an infinite number of possibilities put two words together and make up your own name. I like this idea and I'm sure it's a route with good potential. I don't envisage people paying more than reg fee for such names, because the choices are endless.
As for redeagle. If you must have red then change the bird (hawk, swan ...) If you must have eagle then change the colour/adjective (brown, bold ...)