The Caribbean islands have a very common phrase for this, they call it "cheups", pronounced "chups", and can refer to the sound Peter Griffin makes in the video, or more of a hard, suck-then-stop-abruptly sound by pressing the tongue against the teeth, releasing, then halting airflow very quickly. Both sounds are called "cheups". In fact, the name is so well-known and the sound such a part of Caribbean cultures, they humorously and ironically say the word "cheups" (pronounced "chups") in place of actually making the sound.
Also, in France/West Africa, it goes by another name "Le tchip"
In the USA, I don't think a name has been given a wide-spread name other than "that sound you make when you suck air through your teeth", however, in my experience living in Florida (which has a large Caribbean population), the more preferred naming is "cheups".
If it is useful, based on this post, the IPA defines the sound as the:
"pulmonic ingressive voiceless alveolar fricative ... its symbol in
the IPA would be [s↓].