After a month or so without use I went ahead to use it and the icon and nickname in the console have been changed. My Nintendo account still has the same funds and username, the switch still has the same play activity and games in the same order, just that one change...... what do I do, just change the username name back and change my password? I opened a game with the "new" nickname and it opened just fine and had my save.

I assume you already have multifactor enabled on that account?

No. Because they can't do anything with it, I load it with gift cards and you can only buy games that only go into the console connected to it. Nothing is different other than the console image and nickname. Nothing bought, played. I guess they hacked in to try to get games and then realized they couldn't? But wouldn't they try to do that before changing the console games? AND if the nickname is changed wouldn't the game saves not transfer? That's what's weird, that the saves are the same.

Put 2 factor authentication on anyway. And change your password.

They can play any of your games logging into your account from a secondary console, so they can also buy stuff that they can then play. They can also really mess up your saves. Luckily they can't switch which console is the primary remotely.

How do I change the console username without losing my saves?

You can change your displayed username at any time on the switch, and your id from the accounts page (see below), however your linked nintendo account has to be the same or the saves will go away.

But there's no reason to change your linked nintendo account, just go to
https://accounts.nintendo.com/

sign-in and security settings

You can see sign-in history to see if it was accessed anywhere outside of where you live. Change your password (you will then have to change your password on your switch) and setup 2 step verification. You can also change your sign-in id, but I haven't done that.

That's the thing online everything is the same the only thing that changed was the console icon and account name. Would using a game fly cartridge have caused that?

No, someone would have either had accessed your console (unlikely unless someone is playing a trick on you) or logged in from another switch and changed your icon and name (which you can do from swith user settings). I don't even think you can change your account icon online, though I might be wrong. But in any case it means someone has your password.