Now anyone who has read my blog before will not be surprised to learn I'm looking at the origins of their names, not the religions themselves.
Christianity describes one as a follower of Christ and thus takes that name. Following this back in time we find this as a Germanic translation of Greek khristos meaning 'the anointed', a translation of the Hebrew mashiah and from the Greek verb khriein 'to rub'.
Buddhism, again clearly derived from Buddha, takes the name meaning 'awakened, enlightened'. This comes from budh 'to awake, to know' and related to the Sanskrit bodhati 'observes, understands' and sharing a root with English 'bode' meaning 'proclaim, foretell'.
Hindiusm is from the Persian word Hindu meaning 'Indian' and used both as an adjective and a noun. This in turn came from Sanskrit sindhu 'river' and specifically the Indus river and thus these were 'the region of the Indus'.
Judaism can be traced through the Old French Judaisme, to Latin Judaismus, and to Greek Ioudaios or 'Jew'. In turn this comes from the Hebrew yY'hudah meaning literally 'celebrated' and traditionally held to be the name of Jacob's fourth son from whom all Jews are descended.
Islam is an Arabic word meaning 'submission', this to the will of God. It comes from the root aslama meaning 'he resigned, surrendered, submitted', this is related to salima 'he was safe' and related to salam 'peace'.
Taoism is a religious system founded by Lao Tzu in the 19th century. Here the basis is Chinese tao or 'way, path, right way (of life)' and also 'reason'.
Shintoism is a religious system heralding from Japan and dating from the early 18th century. The term comes from the Chines shin tao, translated as 'way of the gods'.
Polytheism is a belief in many gods, the name from the Greek polytheos. This can be taken further to the Proto-Indo-European pele 'to fill' which has given a word meaning 'plenty' in many languages. There is also the Greek theo, again to be traced to Proto-Indo-European and the root dhes which has given many religious concepts in many languages including Latin feriae, festus and fanum meaning 'holidays', 'festive' and 'temple' respectively.