What is the verb tense for hoping?

Hoping is called a present participle. By itself it is not a verb tense. But:

used with a be verb it could be past or present tense:-

I am hoping to see the Queen when she visits.

or it could be past tense:- She was hoping to get a ride back to work with them.

Used with have / has been it could be present perfect continuous:-

I have been hoping to see you for a long time.

Used with had been it is past perfect continuous:-

They had been hoping for a warm summer.