When named clips are selected and "Bounce to clip" is selected, pre-bounce clip names are deleted in the resulting clip. This is true for MIDI and audio clips.
IMO, this should work similarly to splitting clips. Information should be preserved. In the case of joining two clips, the names should be concatenated left-right and used as the name for the resulting clip. This way no information is lost.
Clips from libraries commonly included useful info "coded" into the clip name. And sometimes I actually create names on my own that I would prefer not be deleted by subsequent operations.