What is the grammatical name and function given to “at the moment of impact”?

At the moment of impact, the eye is left exposed

"At the moment of impact" is called a prepositional phrase/locution. The grammatical fonctions of those phrases are, broadly, that of modification and that of nominal functions. (The preposition "at" is called the head (of the (prepositional) phrase) and "the moment of impact" is called its object.)

It can modify a verb and it has the function of adverbial; it is said to be an adverbial prepositional phrase.

• Those bombs explode at the moment of impact.

It can modify a noun or noun phrase and it has in this case the function of an adjective; it is then called an adjectival prepositional phrase.

• The speed at the moment of impact is that of sound.

There are rarer functions of prepositional phrases (nominal functions mentioned above) and those are their functions when they take on the nature of a noun; they are then assimilated to that part of speech that is called a noun and can have its functions, whereby they are said to have nominal functions. There are six of them.

- Subject
- Subject complement
- Direct object
- Object complement
- Indirect object
- Prepositional complement

• At the moment of impact is the most dangerous time in the whole flight. (subject)

The notions collected above can be checked in these refences: ref. 1, ref. 2, ref. 3. The second and third one are particularly important and should be checked as they contain a lot of instructive examples not given above.

In your example "at the moment of impact" tells when the action of the verb form "left exposed" occurs; it is therefore a prepositional phrase that modifies this verb and it is an adverbial. This kind of adverbial is called an adjunct because it is not essential for the sentence to be grammatically correct: "The eye is left exposed." is a correct sentence (ref.). Finally it can be say that it is an adverbial of time and more precisely an adverbial of time that tells when something happens (there are three sorts: "when", "how long", "how often").