I need to know why is there a comma after "for example" and whats the name for it?

It's always called "comma," but in this case it's a "comma used with an introductory clause." The reason there is a comma there is because "for example" doesn't modify or describe any part of the sentence; it just introduces it. "For example" is always a dependent clause and will most always have a comma after it.

In the case you have mentioned, "for example" is a prepositional phrase used to introduce the sentence, setting the stage, as it were. Therefore, it is referred to as an "introductory phrase." As such, it is separated by a comma (no special name). The preposition is "for" & "example" is the object of the preposition. It is a phrase, not a clause. The rest of the sentence is, of course, an independent clause. (In the previous sentence, "of course" is a parenthetical phrase & is set off by commas.) A clause consists of (at minimum) a subject & a verb. No verb, no clause.

In the case you have mentioned, "for example" is a prepositional phrase used to introduce the sentence, setting the stage, as it were. Therefore, it is referred to as an "introductory phrase." As such, it is separated by a comma (no special name). The preposition is "for" & "example" is the object of the preposition. It is a phrase, not a clause. The rest of the sentence is, of course, an independent clause. (In the previous sentence, "of course" is a parenthetical phrase & is set off by commas.) A clause consists of (at minimum) a subject & a verb. No verb, no clause.