Copy midi part to new track - keep original name?

I would imagine this is a preference somewhere but I cannot find it. Here is the scenario.

  1. Record some midi on a track (for example bass)
    Result = a midi region named “bass”
  2. Copy paste this region to piano
    Result = region is now named piano

What I would like is for the midi region to keep the name “bass” so I can quickly see in my arrange view that the piano is doubling the bass part during this section.

Is this possible?

Pref is Editing>Parts get Track Names.