How do abilities that refer to their cards' names work when the name is changed, or the ability is "stolen" by a card with a different name?
Rayami, First of the Fallen has two abilities:
If a nontoken creature would die, exile that card with a blood counter on it instead.
As long as an exiled creature card with a blood counter on it has flying, Rayami, First of the Fallen has flying. The same is true for first strike, double strike, deathtouch, haste, hexproof, indestructible, lifelink, menace, protection, reach, trample, and vigilance.
My question is related to these rules in regards to Mutate, and the "Top vs Bottom" aspect of the ability.
If Rayami is on top, it seems unambiguous that both abilities would affect her
If she is underneath (i.e. a Mutate creature is played onto her), it seems to me that because this creature is not named "Rayami, First of the Fallen", the second ability will not apply, but the first will (i.e. if that creature dies, it gets exiled with a counter, along with any others that die while it is on the battlefield). So the mutated creature with Rayami's abilities will not gain the abilities of cards exiled with counters on them.
Am I reading this right?