Do I have to choose 2 cards with [Lucemon] in their names or 2 cards with the [Royal Knight] trait among the revealed cards to add to my hand for this card's [On Play][When Digivolving] effect?
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Official Ruling
No, the 2 cards you add to your hand are cards that fulfill either of the conditions: a card with [Lucemon] in its name or a card with the [Royal Knight] trait. Therefore, in addition to the combinations from your question, you can also add 1 card with [Lucemon] in its name and 1 card with the [Royal Knight] trait to your hand.