Does the Father know the Name that will be written on Jesus' thigh?
Much love!
Certainly He does. The Father has not "emptied Himself", and there is no reason to think the Father will not know Jesus new Name, just as there is no reason to think that Jesus will not know our new names, even as it says, no one will know it but the one who receives it.
Again, it is evident that the One Who gives the new name will know what that name is.
But nothing here requires some other meaning to Jesus' 'kenoo', emptying Himself, and these passages
do not force us to deny Jesus' statement at the time, that He did not know the time for His return.
And I am certain that following Jesus resurrection, He received again all He had left behind, and there is nothing He does not know.
So how should we understand these verses, Jesus' Name that no one knows, our new names that no one knows, I would say it's talking about us, and the limited knowledge of man. We won't know each other's new names, but God will. We won't know Jesus' new Name but God will.
We are humanity, not Godhead. And when Jesus became incarnate, when He became the Last Adam, He emptied Himself, and did His works by the Holy Spirit, not by His Own omnipotence.
Much love!