I think "Death Scythe" is just a general term. It's just a weapon that Shinigami-sama is able to use, or is strong enough for him to use effectively. It's also Maka's father's name, in addition to him actually being a completed "Death Scythe," just to add to the confusion.

More of a title than literally turning into a Scythe specifically.

I wonder what Maka's mother looks like. Her pathetic father was going through a divorce because he is a philandering deadbeat according to the hostesses. Maybe we'll get to see her.