Guess the Game Name

Santa Claus needed a vacation. He decided to go to Texas because it was warm and he had heard that the people were friendly.
As soon as he arrived in town, people began to point and say, "Look! The big red one! Isn't he someone famous?"
Santa thought, "Gee, I'll never get any rest if people star asking to sit on my lap and try to tell me things they want."
So he decided to disguise himself. He bought a cowboy outfit complete with cowboy boots and cowboy hat. "No one will know me now, I look just like everyone else!" he thought happily.
As soon as Santa started walking down the street people began to point and say, "Look! It's that famous Christmas personality!" Santa rushed around a corner to hide.
"It's my beard!" he thought. "They recognize me because of my long white beard!" So Santa went to a barbershop and had his beard shaved off. "I really look like everybody else now!" Santa thought. So he walked down the street with a big smile on his face.
Suddenly a man shouted, "It's him! It's him! Look everybody!"
Santa couldn't believe it. He was sure that no one would recognize him. So Santa walked up to the man and said, "How did you recognize me?"
The man looked at Santa and said, "You? I don't know you, but isn't that four-legged guy with the big red nose behind you Rudolph?"