Can anyone ID this bathroom fan motor?
For the most part there are only a few manufacturers of those fan motors, regardless of what brand the fan is. Most of them are interchangeable, but the critical dimension that you often must deal with is the length of the shaft that the fan itself is attached to (and how it attaches). You will need to remove it to determine what you need.

What I have found on the last 3 of these is that the replacement motor costs as much as the entire fan, but the entire fan unit was not going to match the sheet metal work, so swapping it out was more than I wanted to do. So I cleaned the motors and fans really well, put them back in and they worked fine. So far, 3 more years of life on the oldest one. It's worth a try.