Name of Anecdotal Fallacy

I have never seen (it is uncommon) that an anecdote would justifiably be considered fallacious. Typically, this falls in the category of "poor evidence" when use to substantiate a claim. I am not saying that it can never be a fallacy, but is not common enough, in my view, to be included as a named fallacy.

I dissent from Dr Bennett’s answer.  

Most other sources on fallacies list this as a fallacy, and I think it’s one of the 10 or 20 most common fallacies we see these days.  
See, for example,  https://fallacyinlogic.com/anecdotal-fallacy-definition-and-examples/   which says “The anecdotal fallacy is a logical fallacy that occurs when someone argues on the basis of anecdotal evidence. It’s an extremely common type of error found in a wide variety of arguments. Moreover, it is often committed due to a lack of argumentation skills, however, it can be used intentionally as a debate tactic..”

Because someone has an experience that leads to a particular result, the arguer claims that their “anecdote” can be generalized and is proof of a general conclusion.   We see too much of this in the media and Internet.    This is a type of hasty generalization     

Hasty generalization, for sure. But this also enters the realm of proof. At what point do you have sufficient evidence to arrive at a conclusion?

Obviously, hasty generalization is an error in that the evidence is insufficient to arrive at a valid conclusion. On the other hand, I think it is essential to note that we can never be absolutely certain of anything other than metaphysical axioms. Therefore, so we must assign a value to any proposition based upon the available evidence. To dismiss a proposition on the basis it hasn't been proven beyond all possible doubt is fallacious reasoning if one seeks knowledge. We can, however, attain an epistemological certainty, which, loosely restated, means beyond a reasonable doubt, while keeping our minds open to additional evidence or a different interpretation of available evidence.