They are both suitable, but the difference between them is that hereinafter (sometimes written as two words, herein after) usually pertains just to writing within a document, While henceforth is more general, and just means from now on. For what it's worth, I've only ever seen hereinafter in legal documents (my rent contract, most recently).
So, for example, you could say:
Henceforth, we shall not go to 7-11 for hot dogs.
but you could not say:
*Hereinafter, we shall not go to 7-11 for hot dogs.
Within the context of a document, either might be used, but hereinafter specifically limits itself to the document or corpus in which it appears. Therefore, it is often the preferable choice for coining a replacement term or phrase:
Hereinafter[?Henceforth], the hot dogs shall be referred to as exhibit B.
That does not mean that you cannot write henceforth in a document, however. For example, you could write:
In this thesis, I will support the idea that henceforth, all hot dogs should be called hot pigs.
Hereinafter would not be appropriate, since it places too much of a limit on the scope of the author's claim.
Indeed, the correct phrase would be-
This rule allows no exceptions.
The usage of admit in place of allow would sound very odd and is possibly incorrect therefore you should refrain from using it, instead stick with allow.
People who believe that admit can be correct are possibly influenced by the quote:
"No rule is so general, which admits not some exception." - Robert Burton
The context in which Robert Burton said is most probably different to what you think are rules and thus should not be mixed up.
Best Answer
A name is different than a label.
So a label might have your name on it, but often it has something else on it, such as a warning, or description, or classification.
A rule of thumb is that names are unique(ish) and labels are not.
In the example question, it looks like the word you want is "name".
Consider this website: the question's name is the question headline itself: "Is the usage of 'labeled' preferred to the usage of 'named'?". The question's labels are its tags: "usage".
Edit: I just noticed your edit to this question. The third and fourth sentences carry the same meaning as "named". You are "called" by your name, usually. I'd use "named" or go with the fourth option, which just names the method. There are lots of synonyms for "name" but, importantly, "label" isn't really one of them.
Edit 2: Google's built-in dictionary defines label as
This strengthens the notion that while labels are related to names, names are not a subset of labels (though labels might be said to be a subset of names).