Many people want to travel around the world.

To travel functions as a noun because it is the direct object of the verb wants. Am I right?

The whole infinitive phrase does, yes.

What's the whole infinitive phrase?

to travel around the world is the whole infinitive phrase. And you are saying yes that I did get it right being used as a noun

Right.

Actually, in the sentence "Many people want to travel around the world," the word "to travel" functions as an infinitive verb phrase rather than a noun.

The subject of the sentence is "many people," and the main verb is "want." The phrase "to travel" acts as the direct object of the verb "want," indicating what the people desire to do. While infinitive verb phrases can sometimes be used as nouns (e.g., "To travel is my passion"), in this case, it functions as the object of the verb "want."

To determine the function of a word or phrase in a sentence, it's helpful to understand the parts of speech and sentence structure. In this case, recognizing that "to travel" is an infinitive verb phrase can help identify its role in the sentence.