Well, it's definitely not saying people's names, that's confirmed. I don't think we've seen how it does it in the American release for sure. Probably it will say the same thing considering the announcer uses English in the Japanese version. But it's possible that the NA localization team will decide that for native English speakers "The winner is me!" sounds too silly. There have been some differences between the Japanese and English language versions even when it's using English (e.g. "Game!" vs. "Game set!", "Time!" vs. "Time up!"). I would prefer it if it said "Mii Brawler" or whatever, but it looks like it's probably going to be "Mii".
As to why that is... Well, Tomodachi Life has speech synthesis, so Nintendo has done it before. I didn't realize that earlier.
But the Tomodachi Life speech synthesis is lower quality. Like I said, right now good speech synthesis (like Google Translate for large languages) that sounds almost natural is very data intensive, requiring hours of recorded speech. But lower quality can be much much cheaper as far as computer resources. This is ok for Tomodachi Life, they're going for a quirky feel, so it doesn't feel out of place, and having it be able to say the names of Miis provides a lot more benefit to that game than it does for Smash.
Sakurai would've wanted it to sound like the announcer, not the computer-sounding voices in TL. Getting it to sound good and not really jarring compared to the announcer for other characters would be much more data intensive than the synthesis in Tomodachi Life. It is also less essential to the game than it is for TL.
As a side note, profanity censors aren't that hard to get around in things like that. Since it says the words, you just need to come up with something that's pronounced the same way. Such as naming a character "Peeniss" or "Peenuss" or something along those lines. Adding apostrophes between syllables or h's after vowels is an easy way since they will end up unpronounced, so use "suhck" for example. Apply to whatever swear words you like.