These are arbitrary categories that people apply to themselves or to categories of the past. They are not "natural" and as a result have no firm rules or boundaries.

I used Google Ngrams to come up with an interesting chart about the self-definition of ages by technology in the 20th century, in English sources.

Historians do, atleast most of the time. These chronological categories are not foolproof, nor are they set in stone. They are merely tools to better understand history and to make it more workable. Keep in mind that many of these categories, and that includes fairly widely used terms like "Middle ages", are still subject to discussion within historical discourse.

These categories come into life when a historian tries to argue for their importance. If it's properly theorized and put forward in a convincing argument, it catches on and ultimatly finds it way into popular knowledge and general education. Obviously, both popular knowledge and general education are often lagging behind on academic concensus, which is why you'll get a lot of flak from historians for using certain dubious terms. For example, the term "Dark Ages" is still fairly popular outside of historical circles. However, no historian is going to use or support that term.