Final answer:
The name of the structure formed by the facial nerve looping around the abducens nucleus is the internal genu of the facial nerve.
Step-by-step explanation:
The structure formed by the facial nerve looping around the abducens nucleus is known as the internal genu of the facial nerve. The facial nerve, which is responsible for the contraction of the facial muscles, taste sensation, and stimulating saliva production, emerges close to the abducens nucleus, which is the nerve controlling an extraocular muscle responsible for moving the eye laterally. Due to their close proximity, a lesion in the abducens nucleus could potentially affect the adjacent facial nerve, illustrating the intricate connections within the cranial nerve circuitry.