Personally, I wouldn't make the Beatles assumption, not sure if that's an age thing - I am under 30 and I've never listened to a lot of the Beatles. Also, John is a family name for me, so I am used to a lot of men in my life having John as a middle name, so maybe thats why it didn't stand out to me?
Overall I think it's a nice name, both 'classic' names so nothing bad about it, a little plain to my taste, but many people like to stay firmly within bounds of traditional names. Both names are monosyllabic which I don't love sonically, but thats a matter of personal taste and some people love the simplicity that brings. I also think the 'G' sounds from George leading into 'J' of John sounds a little clumsy and awkward to pronouce, but that might be a me thing.