Freeman
Freeman means born-free, as opposed to those born as serfs during the feudal system of the middle ages. So Vincent Anton Freeman is the one who is born freely, without genetic engineering.

Vincent
From Latin vincere "to conquer". So Vincent is a conquerer; a conquerer of his dreams.

Jerome
Jerome means “of holy name”. Jerome is a holy character, one who saves the humanity. In my view, Jerome is the character created by uniting of Vincent and Eugene.

Morrow
Morrow means "the following day". The mission to Titan was at the end of the week, ie, the 7th day. The following day, the 8th day is day that Jerome achieved everything he set out for.
(Note: the working title of the movie was original "The 8th Day")

Eugene
Eugene means “well-born”. Eugene was born perfect, he was born with "heart of an ox", "IQ off the registers", and he was "blessed with all the gifts" but his fate had something else.