What is it called when words in a sentence begin with the same three letters?

There isn't a specific term for when words in a sentence begin with the same three letters. However, it's a type of alliteration, which is the repetition of consonant sounds at the beginning of words.

Alliteration can occur with any number of repeated letters, so your example would fall under this broader category.

It's worth noting that it's not a common literary device, and it's more likely to be unintentional.