Perhaps Luxu never gave Brain the No Name.
- He took Brain's Body
- Brain's heart was sent into the future
- Luxu stayed behind and snuck around Scala Ad Caelum, recording its construction etc
- Luxu switched bodies with someone else, and gave the No Name to someone else
- Ephemer eventually dies
- Luxu continues to switch bodies and watching over everything
- Decades/centuries later, Brain arrives in Scala
- Brain lives for a few decades, having a child
- His grandchild, Eraqus is born, along with Xehanort
- Xehanort is sent to Destiny Islands
- Brain dies
- Xehanort is visted by his Heartless and goes to the future
- Xehanort comes back, then later arrived at Scala
- Just before, or during, or just after his Mark of Mastery, Xehanort meets MoM
- Xehanort completes his Mark of Mastery
- Maybe Odin and the others eventually die, Xehanort gets the No Name
- Decades pass
- Xehanort finds Ven, BBS happens
So Brain never got the No Name, and he was not Luxu's apprentice as he was sent into the distant future.
Brain's keyblade was also the Master Defender, which he gave to Ephemer, so does he still have his own keyblade? Or does he get another one? Perhaps Luxu gives it to him some time after he arrived in Scala, but not in UX. so he might have been the master of it, but far into the future. Then maybe he gave it to Odin, or put it up on that wall before he died/after his grandson was born.