Only Myrkul or the Raven Queen can be a deity at the same time, depending on the setting/pantheon - in the Forgotten Realms, it's Myrkul (replaced by Kelemvor)
All of the information I know of about Myrkul can be found on page 35 of the Sword Coast Adventurer's Guide (this is just the first paragraph):
Myrkul is an ancient god, one of three former mortals who were raised to deityhood when Jergal grew weary of his divine duties and distributed his influence between them. Myrkul became the god of death and the dead, and ruled over the City of the Dead for centuries until he, in turn, was slain. In time Myrkul returned, for can death itself truly ever die? Myrkul's faithful see him as the Reaper, who lays claim to souls and brings them to Kelemvor to be judged.
So it seems as though Myrkul was the god of death, but then was killed, and Kelemvor took over. Then he came back, but didn't really reclaim his previous title; instead, he seems to be an intermediary, claiming souls and delivering them to Kelemvor.
The Raven Queen, on the other hand, is a bit more ambiguous. In the Dawn War pantheon (listed in the DMG, p. 10), she was the goddess of death. The Dawn War pantheon is not the same as the Forgotten Realms pantheon, so I guess there is no Myrkul when she is the goddess of death (as part of the Dawn War pantheon).
In the Forgotten Realms, the Raven Queen is not the goddess of death, but is instead something else. Taken from Mordenkainen's Tome of Foes (p. 58):
Because she was by now a quasi-divine entity, her supernatural rage corrupted the ritual into a phenomenon that took on a terrible strength of its own.
And from page 60:
The Raven Queen's desire to interfere with the affairs of the gods and her subsequent failure was taken as nothing less than treason by both Corellon and Lolth.
This, in the context of her origin story on page 58, suggest that she tried and failed to become a god, which is why she has earned the enmity of Corellon and Lolth. She is now just a "quasi-divine entity", which says to me that this is not a "true" deity like Myrkul.
On the other hand, it does say "divine" again on page 58:
After the nagpas were created and then banished by the Raven Queen, the shadar-kai watched as she fell deeper and deeper into a divine madness.
However, given that she was already described as a "quasi-divine entity", maybe this isn't as interesting as I thought, but I included it for completeness, at least.
So my conclusion is that Myrkul or the Raven Queen is the god(dess) of death depending on whether you're using the Forgotten Realms deities or the Dawn War pantheon. If the former, the Raven Queen isn't actually a true deity, so that would make Myrkul (and Kelemvor) the deities related to death.