Ron, that blue painters tape is definately the wrong stuff. It's designed to peel off easily, leaving no residue. Any moisture (even the high humidity of a freezer) will cause it to release. Plus it doesn't hold ink very well.
What to use depends on how you're wrapping. Ziplocks, for example, take a Sharpie just fine. This is true, too, with foil; except it's often illegible. So on that use labels. Masking tape will do, in a pinch. I just Avery address labels as my go-to, and they work just fine. Again, a Sharpie is more than adequate. These labels work great when freezing in canning jars, too. Caution: Some Avery labels are quick release. Those are just as bad as the blue tape.
If, for some reason, you're dissatisfied with the way a Sharpie works, get yourself one of those pens designed for marking plant labels. They use a darker, more permanent ink than the Sharpies.