It does by implication, otherwise the pre flight action of a commander cannot be carried out, plus the commander has to 'book out'
Nonsense. Art 52 merely says:
The commander of an aircraft shall take all reasonable steps to satisfy himself before
the aircraft takes off:...
There's nothing to prevent two people from both reasonably satisfying themselves that those checks have been made, nor is there a requirement to identify the commander in 'booking out'. And of course very often, the actions themselves
are delegated. No single action required by law uniquely identifies the commander.
In its guidance on logging, LASORS specifically accounts for the case of duties being shared:
Whenever two members of flight crew acting in
the same capacity share a particular operating
duty, each performing such duty for particular
periods only and neither acting under the
supervision of the other, only the time during
which the duty was performed is to be recorded
in the appropriate column of the personal flying
log book.
which suggests to me that the case of sharing duties during a flight is well known and accepted. It is not the case that a single person must be the pilot in command for the entire flight, and it's certainly not the case that a single person must be so designated in advance.