There are tons of checking accounts that pay no interest, or so little (like 0.05%) that unless you carry a very large balance you’ll never hit the $10 1099 reporting requirement. Anyway, entering interest earned on your 1040 is the easiest thing to do, and all tax software programs do it. There shouldn’t be any problems.
As far as not having anyone know about your account, that’s separate from the interest issue. You’ll still need to provide the bank your ID information, whether the account earns interest or not.
You could hide your money in some bank out of the country, but if your balances total over $10,000 you still must report the existence of it via a FBAR to the government, even if it earns no interest.
