Last fall Microsoft/Mojang announced their plan to require all Minecraft accounts to login via a Microsoft account instead of the Mojang account. I believe their stated intention was to eventually eliminate the Mojang account. It was a while ago so I don’t remember all the details, but as I recall the primary reason was for better security.
Earlier this summer a notice began to appear on the Minecraft launcher screen that they had begun to migrate accounts from Mojang to Microsoft. The first time that notice popped up I read the explanation of how to get that done and then waited for my turn.
I have two Minecraft accounts dating back several years. I bought the second one so that visitors here could play with me via LAN even if they did not have their own Minecraft account. Over the years it has not been all that useful because those I play with have their own accounts, but there is no point in worrying about that now.
The reason I mention that here is my second account turned out to be the first one to be migrated. I went through the process and found it relatively easy to do. The only disappointment was the weird name I was assigned for my Xbox gamer tag. It is disappointing that one cannot choose your own tag when migrating. Anyway, I got the migration done the same day that account was eligible.
More recently my original Minecraft account was finally eligible for migration, so I did it same day again. This time the Xbox gamer tag turned out to be the same name assigned years ago when I tried the Windows 10 Minecraft version, which was a bit of a surprise, but after more thought, I think it kind of makes sense. In the process this time I discovered one can change the Xbox gamer tag one time with no charge, but if you want to do it again, it costs $9.99 each subsequent time. Changing names was somewhat challenging, but long story short I eventually got both my gamer tags changed to the same as their on-screen name.
Most disappointing is the fact that there appears to be no way to change the icon that goes with the login. Maybe there is a way I have not found yet. I’ll probably try again sometime when I am looking for some diversion.