What is repetition of consonant called?

The repetition of consonant sounds, especially at the beginning of words, is called alliteration.

Here are some examples of alliteration:

* Peter Piper picked a peck of pickled peppers.

* She sells seashells by the seashore.

* Big bad bear.

There are other literary devices that involve consonant sounds, but alliteration is the most common and widely recognized.