Why it is "the Grinch" but not just Grinch as it's his personal name

The Grinch is not his name. Although it’s not shown in The Grinch, “Grinch” is the name of whatever beast the Grinch is. Were he something else, we might call him the Sasquatch.

But other Grinches are featured in other stories. According to The Hoobub and the Grinch:

Grinches sell Hoobubs such things [e.g. a worthless piece of string] each day.