What you have is the type of hammer I use all the time. The ones with the long tails are usually referred to as French Hammers, and I've heard these referenced by several names. Grind the face of the hammer smooth again and the same with the edge of the short tail.
The former will help you when, for example, you are gonna put a hard sole on some Mocassins or just want to tighten the leather you are going to work with. The smooth face with some cased ( wetted) leather will do a great job for that. It is also great for flattening a seam you just sewed up.
You don't have to smack stuff with it, either. Once smooth, the face of that hammer will make a great "Bouncer"...i.e. a good tool for rubbing stuff when you need to.
Try this next time you make a sheath. Take a look at this seam on a bag I finished recently;
Haven't the vaguest idea why I was taught to make flat seams, but the face of that hammer is crucial.
Don't pound nails with it. The weight of that hammer is meant to enable you to press, rub, and tap,tap,tap.
I use that short little tail several times during the shoemaking process. If you ever make a wet molded pouch out of cow, and you get around to making a wood insert to shape the face of the leather, you're gonna love that little tail for shaping the edges where the seam will go
Hope this helps