Time Machine Issue

I chose a LaCie drive to be the TM for a new rMBP. Before I used it as the TM I changed it's name from "Lacie Setup" to "something different".

When plugged into the mac it shows the correct name and Time Machine shows that it is backing up to the correct named drive ("Last Backup to something different at...") but when disconnected, TM instead says "Last Backup to Lacie Setup at..." Until the drive is reconnected. And on one occasion it would not backup because it could not find the "Lacie Setup" drive even though it was connected showing it's new name.

Any ideas about what is going on? Does this make my backups less likely to be stable?

This is a brand new mac and TM, so I have no issues just wiping the drive and starting anew if that would help. Or is this just a normal variance and it would continue to happen?

Thank you in advance for any help!

 

Thank you so much!

 

Yes, it seems to.

I erased it initially as well, so I am surprised it is that simple. I thought it was a deeper issue or that it was just "the way it is".