Is there a word or phrase for this? When you take a word and extend the sound of a letter - usually a vowel - to intensify it. Sometimes you might say Helloooo and stretch out the ‘o’ sound. What is this called?
It's called (monosyllabic) word elongation or word lengthening.
From The Atlantic Magazine:
Evvvvverywherrrre, from instant messages to texts to tweets and even e‑mails, I see examples of what language watchers call word lengthening. The habit began among teens and 20-somethings, but it is no longer limited to them. Adults are adding o’s to their no’s, s’s to their yes’es, and i’s to their hi’s, to say nothing of a glut of exclamation points. In response to some recent news, my 60-something mom wrote, “LOVE IT AND YOU TOO!!!!” What is going on?
It can be referred to simply as "adding letters to words" or more conveniently as "word lengthening".