if you re-label, the data on the tapes would no longer be accessible (basically a quick erase)
If you re-name the tapes, the new label is stored in the catalog, but not on the tape until the next overwrite operation on that tape, at which time the label is overwritten and the data becomes non-retrieveable
So you could rename then and then move them to an Archive media set that has a permanent protection period
For future use, yes, you should re-label the tape prior to the Month End job.