The signal verb / dialogue tag is the verb that indicates that someone is uttering something, e.g.
I said, “I will survive no matter what.”
She asked, “Aren’t you sick of living like this?”
“You can’t go on like this,” he proclaimed.
I was the sure that I heard the crocodile hungrily mutter, “Dinner time.”
I wrote, “I won’t last the week.”
“Yes you will,” she typed.
Extra information:
If the signal verb/dialogue tag comes before the dialogue/quotation, then a comma is needed between the signal verb/attribution/dialogue tag and the dialogue/quotation, e.g. I wheezed, “Why won’t you leave me alone?”
If the word that comes between the signal verb/dialogue tag and the dialogue/quotation, no comma is needed, e.g. She reassured me that “crocodiles don’t live forever.”
In literary analysis (i.e. in essay and other formal writing), these are usually known as signal verbs. In creative writing (narrative or poetry), these are usually known as dialogue tags.