I see that it's trying to store to MyName's AirPort Time Capsule.local. It thinks there's only 500 GB available, when there should be more.
If the message indicates that 500 GB is available, then 500 GB is available. If you need more available space, erase the Time Capsule disk and you will have 2 TB or 3 TB available, depending on which version of the TC that you have.
Chances are, you will never need all the old backups from months and years in the past, so my recommendation would be to erase the Time Capsule and start over again with a new backup and move forward. Post back if you need more step by step help with this.
It's the local that's confusing me.... is TimeMachine trying to store on the MacBook instead of to the Time Capsule?
The .local simply means that the Time Capsule is on the same home network that your MacBook Pro is using. This is normal, correct and expected.
I'm getting daily messages that the backup hasn't completed.
One possible reason for this is that your Mac is trying to back up to the "old" existing back up file on the Time Capsule, which has possibly become corrupted and is no longer useable.
If you still want to try to continue to try to back up to the "old" backup file on the Time Capsule rather than simply erase the Time Capsule and start over........
Hold down the option key on your Mac and click on the Time Machine "clock" icon at the top of the screen
Select Verify Backups
Run the verification check, which might take anywhere from 10-60 minutes or more depending on how much data is stored on the Time Capsule disk. Let the process run until it completes, or until you see an error message.
If a message appears, post back with the exact text of the message.
You can watch the progress of the verification check by clicking on the Time Machine "clock" icon at the top of the Mac's screen and then clicking on Open Time Machine Preferences.
