I've had the impression that Garland Hammer Company (
http://www.garlandmfg.com/mallets/split.html) originated this design. They are, anyway, still in business. You can get new faces directly from them at the site I listed, or go on Amazon or suchlike places. Lots of choices.
I have a couple of these in different sizes. I use the small one regularly as a chisel mallet, even though the plastic heads are nearly worn out. I like the combination of weight and soft face.
The larger one has been on the sick list since I got it, because some past fool had used the side of the head to bash on things, and the casting got distorted there; yet another project on the multi-page list. Make sure the two parts meet pretty well along their length (looks like you need a little filing on the ends, on the side in your pictures), and the nut tightens up properly.
Yours is not a Garland - they're proud of their hammers, and the name is prominent on the heads - but if the size is consistent with Garland's, their inserts should work.