I like the Pepper Moon restaurant

[snoopya1984]

Is this correct?or should the definite article be omitted?

[bhaisahab]

Is this correct?or should the definite article be omitted?

It's OK with or without the article.

[emsr2d2]

Is this correct?or should the definite article be omitted?

If the restaurant is actually called "The Pepper Moon" then you should leave the article in as it forms part of the name.

If the restaurant is called "Pepper Moon" then it's optional as bhaisahab said. I prefer it with the article if you're going to use the word "restaurant" directly after the name.

I like the Pepper Moon restaurant.
I like Pepper Moon. It's a great restaurant.