Although there are no universally recognized "titles" for those who devote themselves to la santisima muerte, there are a couple of them that I've seen used. It should be noted, however, that these personal descriptors are not in any way a sign of an established priesthood or organization and can be used by anyone who has developed a strong connection to la muerte.
Quick Spanish lesson for all of us Anglophones. "La Muerte" is the Spanish word for Death. Although is doesn't have the traditional "a" ending, it is a feminine word, denoted by "la". This may be a contributing factor as to why "Saint Death" has manifested in Mexico/Central America as female. One of many. Maybe, maybe not.
"Santa Muertero" for men, "Muertera" for women. Muertero/a is a Spanish word for someone who works very heavily with the dead, the muertos. (When you add "-ero/a" to the end of a word in Spanish, it's kinda like adding "-er/-ess" to the end of an English word, making it "someone who does this.") Now, add "Santa" to Muertero, and you have "someone who is devoted to/works with Holy Death. "Sta" is the abbreviation for "Santa," which I personally like because everyone in the English speaking world thinks of Santa Claus when you write out Santa. Lol.
Another descriptor you'll see is "Santa Muertista" which usually only has the "a" ending. Personally, this seems like a borrowing from the term Espiritista as a general Spanish word for a person who works with spirits. Espiritista is used throughout the Spanish-speaking Caribbean islands (but is also found in Mexico, possibly due to the Cuban diaspora, which is also why you see Lukumi and Palo there) as one who is accomplished within the realm of Espiritismo, their version of Allan Kardec spiritism (which is a whole other ball of wax!)
So, Santa Muertero/a or Santa Muertista. Take your pick. And I'm sure there are probably others out there I've yet to encounter. La Santisima Muerte is very quickly growing, changing, expanding, and one never knows exactly what to expect from her.