You cast the spell as part of the resolution of Ryan's triggered ability. You can't wait and cast the spell at a later time.

If something refers to your commander while you have two commanders, it refers to one of them of your choice. If you are instructed to perform an action on your commander (e.g. put it from the command zone into your hand due to Command Beacon), you choose one of your commanders at the time the effect happens.

Although Doctor's companion is a new variant of the partner ability, the rules for partner have not otherwise changed. Notably, Time Lord Doctors and cards with Doctor's companion do not interact with cards which have another partner ability.

The Doctor's companion ability allows you to have two commanders if one has the ability and the other is a legendary creature that is a Time Lord Doctor and has no other creature types. Creatures with the changeling ability, for example, can't be a second commander this way.

You may pay optional additional costs to cast that spell, such as kicker costs. If it has any mandatory additional costs, you must pay those.

Once the game begins, your two commanders are tracked separately. If you cast one, you won't have to pay an additional the first time you cast the other. A player loses the game after having been dealt 21 combat damage from any one of them, not from both of them combined.

If your Commander deck has two commanders, you can include only cards whose own color identities are also found in your commanders' combined color identities.

An effect that checks whether you control your commander is satisfied if you control one or both of your two commanders.

Both commanders start in the command zone, and the remaining 98 cards (or 58 cards in a Commander Draft game) of your deck are shuffled to become your library.