What is the term used...

alliteration?

Thanks! Was on the tip of my tongue (for days), but just wasn't coming to me.

I think alliteration just means if an initial letter sound is repeated, not necessarily if all the words begin with the letter.
"She sell seashells by the beach" is still alliteration.

alliteration is for repeated *initial* consonants, as in the example above, consonance for repeated consonants *elsewhere* within words, and assonance is for repeated *vowel* sounds.

Yes thank you so much. I'm going into my junior year [high school] and doing my AP English homework i could not for the life of me remember alliteration. I knew it started with an 'a'!

Note, too, that it doesn't necessary have anything to do with letters:

Psychiatrist Cindy sins.

Ken cuts quiche.

(etc.)