Well, the song DOES say "You're a mean one, Mr. Grinch" so I'd hazard a guess that it's his family name. Does make one wonder what his first name is.
Also, I am reminded of that bit in the Daffy Duck/Porky Pig cartoon where the murder is interviewed:
Porky Watkins: Name? Speak up, old boy.
Shropshire Slasher: Shropshire Slasher.
Porky Watkins: Occupation?
Shropshire Slasher: Shropshire Slasher.
Also, I am reminded of that bit in the Daffy Duck/Porky Pig cartoon where the murder is interviewed:
Porky Watkins: Name? Speak up, old boy.
Shropshire Slasher: Shropshire Slasher.
Porky Watkins: Occupation?
Shropshire Slasher: Shropshire Slasher.