I want to connect a 2TB external hard drive to my airport extreme with time machine. I can't find any instructions for how to do it.
Please take a look at this Apple Support document for information and instructions:
https://support.apple.com/en-us/HT202784
I think one obstacle is that my router has a different name than anything else in my Apple system.
It does not matter what the name of your AirPort Extreme might be as long as the name does not exceed 26 characters. Fewer would be better.
Note.....the USB port on the AirPort Extreme is an old and slow USB 2.0 design, and the processor inside the AirPort Extreme will limit speeds to about half of normal slow USB, so backups are going to be S--L--O--W and not all that reliable.
Backups will occur much more quickly and more reliably if you connect the hard drive directly to your Mac and back up that way.