Trying to type my bank's name in so the system could find it for the 1099-INT system could not find in its list of supported banks

If your bank is not supported, you can choose "I'll type it in myself" in the bottom right corner.

This is also happening to me with my CD version I have installed on my PC.

I have 6 accounts at one banking institution so it's a real chore to try to figure out where to type in all those figures.

However, I tried the Online version and the bank actually DID appear in THAT LIST...and it imported all the 1099-int, 1099-div, 1099-B, and the 1099-misc information too.

I have tried but cannot get an answer from TurboTax on this.

Yes, you are correct. There are differences between TurboTax CD/Download and TurboTax Online to cover a vast range of customer needs. I suspect your unexpected results could relate to system updates.