What is the grammatical term for two or more words next to each other that begin with same letter?

There isn't a specific grammatical term for two or more words next to each other that begin with the same letter. This is a literary device called alliteration.

Alliteration is the repetition of the same consonant sound at the beginning of words or stressed syllables.

For example:

* Peter Piper picked a peck of pickled peppers.

* She sells sea shells by the sea shore.