Is the simple sentence okay?

How about: The boy, Jack, travels a lot in the United States.

Thanks.

Are you telling me that sentence is correct both in grammar and in meaning (dull though)?

A boy named Jack travels TO a lot of places in the United States.

slightly different meaning
A boy named Jack travels a lot of places in the United States.

The second sentence indictes that the travel is continuing

Thank you.

Have you given me the feeling that the sentence "The boy named Jack travels a lot of places in the United States" is correct?

Why not use "the" there?

You would use "The boy..." if you wish to denote a particular boy called Jack who had already been mentioned, either directly or indirectly, and you would use "A boy..." if you were mentioning him for the first time.

I met several young people on my trip. [Among them] The boy named Jack had red hair and was very tall.

A boy named Jack once told me he smoked cigarettes when he was 9 years old.

We don't say "travels a lot of places". We travel to lots of places, or we travel a lot.