mid-15c., from Latin eulogium, from Greek eulogia "praise; good or fine language" (in New Testament, "blessing"), from eu "well" (see eu-) + -logia "speaking" (see -logy). Eu legein meant "speak well of."
-ist
word-forming element meaning "one who does or makes," also used to indicate adherence to a certain doctrine or custom, from French -iste and directly from Latin -ista (source also of Spanish, Portuguese, Italian -ista), from Greek agent-noun ending -istes, which is from -is-, ending of the stem of verbs in -izein, + agential suffix -tes.
Variant -ister (as in chorister, barrister) is from Old French -istre, on false analogy of ministre. Variant -ista is from Spanish, popularized in American English 1970s by names of Latin-American revolutionary movements.