Tar-Alcarin was the 17th ruler of Númenor (LotR/1035, UT/222). His name is simply the shortened form of alcarin(qua) “glorious”. Alcarin “Glorious” was also a sobriquet for Atanatar II, the 16th king of Gondor (LotR/1038, 1045).
Quenya
alcarin(qua)
adjective. glorious, brilliant, glorious, brilliant, [ᴹQ.] radiant
alcarinquë
proper name. Glorious
alcarin
proper name. Glorious
alcarin
glorious, brilliant
alcarin adj. "glorious, brilliant" (shorter form of alcarinqua, q.v.) (PE17:24), hence Alcarin masc. name (or title) "the Glorious", title taken by Atanatar II of Gondor, also name of one of the Kings of Númenor (Appendix A).
-inqua
glorious
-inqua adjectival ending, seen in alcarinqua "glorious" (WJ:412) from alcar "glory". Etymologically, -inqua means "-full", like "glory-full" in this case. A variant *-unqua is implied in WJ:415 (only referred to in archaic form -unkwā). "The forms using u were mainly applied to things heavy, clumsy, ugly or bad", whereas -inqua (in the same source derived from -inkwā) is neutral.
A star (S/45) or possibly the planet Jupiter (MR/435). Its name is simply the noun form of the adjective alcarin(qua) “glorious”.