Assuming it is not a forest for the trees thing (looking at https://www.gamesradar.com/mario-party-3/cheats/
it mentions if you fail to give it names you get Nintendo ones, now I don't know where this part is in the game or if it is a high score entry or something) then that seems doable, though probably in more of a "easy once you know how".
If it is not user selectable then the names will probably exist either as text or as graphics (graphics are more colourful than most text engines, can be big, and for short menu things in low text games it is often graphics). You then get to figure out what that might be.
If it is text and there is the option to enter some form of name like the faq implies then it can complicate things as they might have placeholders where the names are at, or the placeholder text gets harder to find. If you only want this hack for you and yours and are prepared to use given characters or control ports (don't know which it will be) then you can try overwriting the placeholders with names.
You can try simple things if you want before having to learn all the hacking if you don't want to/have time to. These are anything but foolproof (compression, devs not acting predictably, some complicated setup) but work often enough across various systems that we still use them all the time when peering into the guts of ROMs.
1) For text then try relative searchhttps://www.romhacking.net/utilities/513/
Don't go straight for the names, or if you do expect it to work, but a longer bit of text if you can. If it is relative then hopefully you found the encoding with the tool just then and can then go on to find the names.
2) For graphics play with a tile editor and see if it is graphics.
We have fancy ways of finding data in a ROM but it is still quite viable to load up a tile editor, set it N64 modes and press down/page down a lot to go through the entire ROM, repeating as necessary for the various modes.
I don't know what we are suggesting for the N64 these days.
In both cases there are some more advanced things you can be doing (say for the relative search then if there is a variable, "you need ? stars to unlock this" sort of thing) don't include that in a search as the variable might throw it off, search for the text from either side of it though. For graphics an emulator will probably be able to tell you something about what it is if you look at it in the various viewers or indeed some results with the tile/oam/bg/2d/whatever viewers tell you it is likely not graphics you are looking for in this case).
Once you know where it is and how it is formatted it is probably going to be quite easy to change things but the trick is getting to that point.