Ok, comparing, here are the equivalent apps on my phone (A Pixel 6 from Google) Messages, Gmail (admittedly not "Mail", despite working with non Gmail email addresses), Calendar, Wallet, Home. That's a total of 1 character in difference.
These have longer names, clarifying e.g. "Google Wallet" if you go look at them on play store or something, but the actually displayed names that you actually see when using your phone are pretty much identical to iOS.
Other non-branded names include Calculator, Camera, Clock, Contacts, Docs, Files, Fit, Maps, News, Photos, Safety, Settings, Translate.
Branded names that I believe came with include Chrome, Google, Google One, Google TV, Play Store, and YouTube. Frankly I think it's pretty appropriate that all of those come with branding.
But these apps don't need to be branded due to being a monopoly.
Google's approach is better (if they didn't butcher the naming every time and kill apps constantly) for the consumer as it indicates you have choices.
I wish someone would make a platform that takes that idea to the next level:
Your spreadsheets? No, they're not in Excel® or numbers.app or OpenOffice. They're in "Spreadsheets".
Same with documents: Not in Word or pages.app or w/e. They're in Documents.
Want to browse the web? No Safari or Firefox or Chrome names. Click on the icon that says "Web browser".
Your e-mail? Click the shiny "e-mail" icon.
(note: this is more about shielding/releasing the user from having to worry about underlying technologies. Basically, the "it just works" taken to the next level)
iMessage is the e2e protocol used by the messages app if you're texting another iOS user. Messages is the name of the app that does that, as well as SMS.
It's really nothing that most end users notice or care about, as long as they get their blue bubbles and fun features.
At least two countries, I think. You're probably thinking of the US, but SMS is alive and well in Canada. (FB Messenger is #1 but far from monopolizing Canadian habits.)
And it shall be called "hangouts".