Incidentally, the standard meaning of surendra is indeed lord of the Gods as the meaning on this site states. indra is standardly derived from ind whose meaning is claimed to be strong, but that is unattested in old literature, and is often taken to be a backformation. The intended meaning is probably a root related to ud/und to flow (etymologically related to the IE root of English water) and seems to mean to drop. -ra is the instrumental affix, and indra is the rain god. In Rgveda, one sees an older stratum with varuNa (the enveloper: sky god in this period, but later sea god) replaced by indra. indra is the central figure in vedic mythology and when the trinitarian Hinduism developed, was preserved as the king of gods (his origin as the rain god maintained only in his being the possessor of thunder). From the earliest phase, indra had a connotation of chief amongst or ultimate possesor of and is a very common second element in names.
sura (with a schwa like the first sound in about at the end) means god: again the etymology is unclear. It may be a backformation from asura (powerful) which had at some point developed a negative connotation, or it may have something to do with words like svar for bright. (The verbal root sur, to lord, is probably a nominative.) surendra is the chief amongst gods, and is a common term for indra, and has been long used as a name. (Hows that for a recursive use of indra?)
surA (with a long open A as in car), on the other hand is derived from su (originally meaning to press out, but from its specialization of pressing out a religiously important drink soma form a plant, also later meant to prepare drinks, i.e. to distill) and does indeed mean alcohol. surendra can technically, therefore, also mean ultimate possessor of alcohol. In fact, mythology did connect surA and sura: the story goes that the sura were rather fond of surA, and that's how they got their name.
sura also means a musical tone (should properly be svara) ultimately from svR, related to the Indoeuropean root of swarm. surendra has occasionally also been used to mean the ultimate possesor of musical talent.