Latin fidēs comes from a root meaning to trust, which also gives confide, fidelity and — by a longer road — federal. Faith in Latin is originally something between two parties rather than something held privately.
The English name Faith belongs to a specific and quite datable episode: the Puritan enthusiasm for virtue names in sixteenth and seventeenth century England, which also produced Hope, Charity, Prudence, Patience, Mercy and a good many stranger ones that did not survive. Faith, Hope and Charity are a set, taken from Paul's letter to the Corinthians, and were sometimes given to three sisters.
Arabic īmān is among the most widely used girls' names in the Muslim world, and denotes faith as conviction and assent. Sanskrit śraddhā is subtly different again — closer to trust or earnest confidence, and in the Vedic material it is personified as a goddess.
Greek pístis completes the set, and like the Latin carries an original sense of trustworthiness in dealings as much as belief in doctrine.