Do you think with different naming or branding it would've been any better? I'm not sure it would - I think the big thing is that they've tried to move from a (legacy) Windows-heavy language/runtime to one that is more cross-platform, and that is inevitably going to be tricky no matter what you call it.
I think the naming does make sense, it's just been maybe been poorly communicated, because I've seen a few people getting tripped up by it.
The projects would be roughly the same, but information about them would be significantly cleaner
If I see an article about .NET, depending on the year it might be about 2 different product lines, because the shorthand was made to be the same
If I need to google how to X in Visual Studio, more than half of the results will be irrelevant, because they will be about a different product, so on and so on
If the naming was good, it wouldn't trip up people (So regularly at least), that's my point
Other ones that trip up people, Teams for personal use?, that one regularly bugs out when interacting with business users?
Skype vs Skype for Business?
That does introduce some ambiguity, I just don't know how often people google things like that. And if searching "how to authorize HTTP request .NET" (or similar) is a common occurrence, I reckon there's a bigger problem lurking beneath the surface there...
It's worse on less formal communication, but shorthand "We're targeting .NET" might mean
"We're targeting .NET (Standard)" (Which works on both Framework and used to be Core / current .NET)
"We're targeting .NET (Framework)" (Used to be shortened to .NET)
"We're targeting .NET" (Formerly .NET Core) / (6/7/8/9), current recomendation being to call this one just .NET (But not always respected, and not retroactively applied
If legacy wasn't a thing, there wouldn't be much trouble, but since many libraries and some functionality does get backported, you might be stuck with documentation doing any of them, maybe even inconsistently
I think the naming does make sense, it's just been maybe been poorly communicated, because I've seen a few people getting tripped up by it.