Honestly, I think the father needs to unplug from the videogame for a month or so and get reacquainted with reality. Maybe take some time outdoors, hug some trees, or even dig a hole and plant his Xbox in it. Feeling he has the "right" to name his children informs all of us that somehow Minecraft has transported him back to 1822 and not 2022.
No, naming rights is the least of his current problems. The key one as I see it, is that Minecraft is not real. It's an articifcial environment that millions get absorbed into - but thankfully - re-emerge a few hours later. He seems to be losing that ability.
Jeb and Notch are not godawful names or anything - but the mom is 100% right, their connections to a video game will bring grief to the twins. Only slightly better than naming one of them SpongeBob.
All is not lost though for the dad. He can always petition the courts to change his name to Notch - sort of test it out for a bit and see what response he gets.