His alias while travelling was Mr Underhill, but he was referred to by many names.
Frodo is referred to by several names and titles in The Lord of the Rings. On leaving the Shire he uses the alias 'Mr Underhill'. Gildor Inglorion calls him 'Elf-friend' in acknowledgement of his ability to speak Elvish. After the Council of Elrond he is given the title 'Ring-bearer'. After the fulfilment of the quest he is referred to by the bards as 'Nine-fingered Frodo' or 'Frodo of the Nine Fingers', after Gollum, in an effort to steal The One Ring, bit off his finger in order to get it off of the invisible Frodo.
Frodo is the only prominent hobbit whose name is not explained in Tolkien's Appendices to The Lord of the Rings. In his letters Tolkien states that it is derived from Old English fród meaning "wise by experience". A character from Norse mythology called Fróði is mentioned in Beowulf, where it is rendered in Old English as Froda. Tolkien did mention he changed final a's to final o's in male Hobbit names.
In the early drafts of The Lord of the Rings the principal character is called Bingo Baggins; the name Frodo is given to another hobbit. In the drafts of the final chapters of The Lord of the Rings published by Christopher Tolkien as Sauron Defeated, Gandalf names Frodo Bronwe athan Harthad (Endurance Beyond Hope) after the destruction of the Ring. Tolkien states that Frodo's name in the fictional language of Westron was Maura Labingi. His name in Sindarin (another of Tolkien's invented languages) appears to have been Iorhael, which is derived from ior meaning 'old' and hael meaning "wise". In The Return of the King he is also referred to by the name 'Daur', a Sindarin word meaning "noble"  (or perhaps "Wise by experience," if it means the same as "Frodo" does.)