"one who demands anything as a right," 1747, from claim (v.), on model of appellant, defendant, etc., or from French noun use of present participle of clamer.
Entries linking to claimant
claim v.
c. 1300, "to call, call out; to ask or demand by virtue of right or authority," from accented stem of Old French clamer "to call, name, describe; claim; complain; declare," from Latin clamare "to cry out, shout, proclaim," from PIE root *kele- (2) "to shout." Related: Claimed; claiming.
Meaning "to maintain as true, assert a belief or opinion" is from 1864 ("A common use, regarded by many as inelegant" - Century Dictionary, 1895); claim properly should not stray too far from its true meaning of "to demand recognition of a right." Specific sense "to make a claim" (on an insurance company) is from 1897.