GMAC Bank — the troubled mortgage and auto giant that gained bank-holding company status in December — officially reintroduced itself as Ally Bank on Friday.

The rebranding comes after months of research to determine how best to position the bank and to structure its products. For starters, the name is meant to connote trust. Seems like a wise move for a bank that will likely have a $20 billion government tab when all is said and done.

Here’s what strikes me as problematic: Ally Bank offers CDs and money market accounts with some of the highest rates around, all without minimum-deposit requirements.

Take a look at the comparison on its web site for its online savings account:

Ally: 2.25%
Chase: 0.05%
Wells Fargo: 0.05%
Bank of America: 0.10%
ING Direct: 1.50%
HSBC Direct: 1.65%

And here’s a comparison of money-market account rates:

Ally: 1.90%
Chase: 0.01%
Wells Fargo: 0.05%
Bank of America: 0.50%

Ally is 60 basis points higher than its nearest competitor on savings account rates, and 140 basis point higher on money-market account rates. Ally has said it can offer higher rates because of its web-only presence. But Ally’s APYs are still higher than other web-based competitors’, like ING Direct.

Will the bank succeed in garnering more business? You bet. My concern is the cost at which that business will come. You see, irrational pricing upsets the lending equilibrium. It seems like over-aggressive lending tactics are what got this financier in trouble in the first place.