You can rename a bus at the moment it goes into a Hierarchical sheet.
So on the top level sheet you name the bus: IN_[0..63], and in the hierarchical sheet you name the bus OUT_[0..63] and then connect the bus on the top level to the hierarchical sheet connector.
A while back I posted an example project with all sorts of bus behavior in:
For posting on this forum, the forum software does some unfortunate translation. When you type two dots (which is what KiCad needs in a vector bus) then it displays three dots after submitting your post. You can prevent this by enclosing the name with backticks as both Qu1ck and I did.