I'd say sweep (if you completely clean/close the account) or withdraw (if account remains active)

I see transfer more for transacting with others

withdraw too generic
sweep (have no idea what does mean)
tranfer (makes more sense but may confuse with transfer out)

Some options (don't thinking anyone is perfect, just dropping there)

move?
internal move? (too long but more specific)
Internal transfer (variant)
self-transfer (could be confusing too)

is there any word combining "internal" and "move" ?