In SH3Cmdr Release 2.2, click on "SH3 Options" and select the "Use real ship names in patrol logs" option. Provided all patrol logs were created in the same language as you currently have selected in SH3, they'll all be updated the next time you create a Personnel File for the selected Commander.
If you want to wait a few days, SH3Cmdr Release 2.3 expands on this by not replacing the default SH3 name, but adding a real ship name, so the result is something like: "S.S. Minnow (C3 Cargo)". A few people asked for this enhancement...and they got it!