Which kind of illustrates the futility of determining an official demarcation. Some of the current South End, all of JP/Roslindale/West Roxbury were once part of Roxbury. I'm not sure it's ever clear what precisely constitutes modern Roxbury.
I've ranted about this frequently on here, but the modern era has seen an unprecedented ossification of spatial reality. That is, every square inch of land is defined, ordered on some "level" (sub-neighborhood, neighborhood, city, etc) and stays that way for eternity. The idea of even national borders is only the product of imperial regimes, for the most part. And it wasn't until very recently in history, with few exceptions, that cities or towns had any "official" borders (except for the borough towns and city states). Then, only within the last century, you have the rise of formalization of boundaries of areas that once had not "official" border beyond whatever the commonly held opinion was of the people who lived there.
Jamaica Plain is a great example: there never was a "town" of Jamaica Plain; it was just an area of West Roxbury, previously of Roxbury. And of course areas surrounding major, named intersections also used to be their own thing—Forest Hills, Cleveland Circle... are these "neighborhoods" of JP or Brighton? Not really, since they straddle different neighborhood and moreover they kind of have an identity (to a local) that transcends "ranking" them in the "neighborhood > town > state"ordering system that encompasses every piece of land today.
And areas and identities do shift over time. Modernity keeps everything "stuck"; neither (formal, at least) national nor neighborhood borders ever change, which has positive and negative aspects. Jamaica Plain is never going to grow bigger than it is, no matter how many JP expats move just over its borders. As for Roxbury, you might make the case that "Roxbury" as an identity is a lot smaller now than it once was. This gets tricky, however, because the forces behind the fact that people now identify Lower Roxbury as "the South End" (ditto for people thinking Mission Hill is part of JP, not Roxbury) are reflective in large part of racial and economic implicit biases. Roxbury is associated with black people and crime, and the South End is associated with gentrification and white people. Realtors know this; back in my apartment-hunting days it was comical (if not depressing) to see how far realtor ads would go to avoid saying the advertised building was in Roxbury. So this is the aspect of neighborhood name flexibility that should give us pause, since the main valid argument against just going with the flow and letting people's local, if technically inaccurate, perceptions of neighborhoods is that this basically allows a 'colonization of territory by naming" to happen, where the inevitable pattern is that wealthy or gentrified (and usually white) neighborhoods expand into territories associated with minorities and poverty.
Interesting to also note here that Longwood Medical Area is all Roxbury and that's not even a particularly historical designation—the housing group that fought Harvard Medical School and BWH's expansions in the 60s was and remains the Roxbury Tenants of Harvard. I do wonder what someone would have called the LMA "proper" back in, eg, 1960—anyone know? LMA wasn't a term back then, so eg, if someone asked the principal of Windsor School in 1960 what neighborhood it was in, what would they say? My guess is the response would be yet another example of fluidity of geography: "it's on the border with Brookline". Sometimes, the best way to describe something is by describing what it's close to, rather than defining what it is.
Anyway, I think the naming stuff is really interesting and agree with
@HenryAlan that people get too hung up on what things technically are or are not, but still, there are other factors that are hidden away in what we choose to call our urban territories and they are important to consider as well.