Identifying infinitives

I have [to go there].

I must [go there].

In these examples, the bracketed elements are subordinate infinitival clauses functioning as catenative complement of "have" and "must".

The sentences as a whole are called the matrix clauses, within which the infinitival clauses are subordinate.

Thus, you could if you wished call "have" and "must" the principal or main verbs, since they are the verbs of the upper (matrix) clauses. But those are just general, not grammatical, terms. Grammarians would call "must" and "have" the matrix verbs, and "go" the subordinate verb.

Note that the subordinate (dependent) clauses can be dropped, for example

A: "Must you go so soon?"

B: "Yes, I must"

I like to go there.
I want to go there.
I need to go there.
I have to go there.

Under a traditional analysis, "like", "want", "need" and "have" are all main verbs in these examples.  The verb "to go" is a full infinitive.  The infinitive phrase "to go there" is the direct object of the main verb. 

I can go there.
I will go there.
I should go there.
I must go there.

Here, "can", "will", "should" and "must" are all auxiliaries. The "go", which is a bare infinitive, is called the main verb.

The reason they are called main verbs has to do with the way that conjugation was traditionally taught:

I have to go there.
I had to go there.
I will have to go there.
I might have had to go there.
I could have been having to go there.

I go there.
I went there.
I will go there.
I must go there.
I will be going there.
I could have been going there.

All of these conjugated verb start with a finite verb form and, if they continue, only contain participles and bare infinitives thereafter.  Once you reach something else, such as the "to" of a full infinitive, you've gone past the end of the conjugated verb.

The verb have is a tricky little thing.  Sometimes it's an auxiliary to some main verb.  Sometimes it's a main verb with its own auxiliaries.  In "could have been having", it appears once in each role.

It's also tricky in that, instead of having its usual possessive sense, it carries obligatory semantics when it is followed by a full infinitive.