Haber how to use. No what is the name of the form of the verb that goes with haber in phrases. Like he dado de estsdo. Etc

Hola James

The second part of the verb in perfect tenses, e.g. he ido, has comido, habéis venido, habías cantado... is called "past participle" (participio); regular past participles end in -ado or -ido, but there are some that are irregular that have different endings, like hecho, dicho, puesto...

Here is a bit more information, have a look.

I hope that helps.

¡Feliz Año Nuevo!

Inma