Why is 'verb to be' not called 'verb to is am are'?

My own hypothesis is that being, issing amming and areing were once separate verbs, but the different finite forms were kept for redundancy

The verb infinitive is (to) be. 

Will you be late?

to talk

to walk

to think

to sing

to sit

etc.

Because the verb "to is am are" would sound really stupid.

English, like other languages such a Spanish and French, once had different forms of verbs depending on the subject. However, over hundreds of years, speakers of English simplified the verbs, and we lost most of the forms except for the third person singular "s" (I run, you run, he/she/it runs). Even that seems to be dying.

The more frequently used verbs kept their irregular endings. "be" is the mostly commonly used verb, so it kept the forms "am, is, are" and the infinitive form "to be".  "Be" is used in many ways- after modals (will, would, can, could, may, might, should, and must), and in the participles "being" and "been". 

Although it is irregular in the present tense it falls into the pattern of I will be, They will be etc and the only meaningful form of the infinitive is to be (or not to be).

be, as a general concept, is exist but with a general concept of identity.  Why is the verb so irregular?  Bad planning on the part of the inventors of the language, perhaps.  Really more a case of "so common in use that it never changed as the rest of language changed" though.

The question itself is simply a case of why do we call things the way we call them?  Well, because that is how it came to be.  Gotta call it something.  Who decides?  Not clear who decides such things.  Existential questions of little actual import.