From Fensome et al., 2019:

"Compositosphaeridium", Erkmen and Sarjeant, 1980, p.65–66.
Name illegitimate -- senior homonym: Compositosphaeridium Dodekova, 1974.
Taxonomic senior synonym: Compositosphaeridium Dodekova, by implication in Lentin and Williams (1981, p.53), who included the "type species" of Compositosphaeridium Erkmen and Sarjeant, Compositosphaeridium bulgaricum, in Compositosphaeridium Dodekova. Erkmen and Sarjeant cited the generic name as "Compositosphaeridium Dodekova, 1974" but gave the "type species" as "Compositosphaeridium bulgaricum Erkmen and Sarjeant sp. nov., nom. nov. pro Compositosphaeridium costatum Dodekova, 1974, non Davey and Williams, 1966 [1966b herein] ...." Since a type once designated is permanently attached to a name except through formal conservation (ICN Article 7.2), Erkmen and Sarjeant (1980) effectively and validly published a new generic name, Compositosphaeridium Erkmen and Sarjeant, which is an illegitimate junior homonym of Compositosphaeridium Dodekova.
Type: Dodekova, 1974, pl.1, figs.4–6, text-fig.1, as Compositosphaeridium costatum, designated by Erkmen and Sarjeant (1980, p.67).