Latin vīvus, Greek bíos, Sanskrit jīva and the quick of older English — as in the quick and the dead — all descend from one Indo-European root meaning to live. Names built on it run through every branch of the family.
Hebrew ḥayyim gives the feminine Ḥayyah, and the name Eve — Hebrew Ḥawwāh — is glossed in Genesis itself as mother of all living, the text making the connection explicitly. Whether that gloss is the actual etymology or an interpretation attached later is debated, and this site would rather tell you the debate exists than pick a side.
Sanskrit jīva carries a philosophical charge the European words lack: in Vedantic and Jain thought the jīva is the individual living soul, so a name built on it is not simply about being alive.
Arabic ḥayāt is among the most widely used names in the Muslim world, and belongs to the same Semitic root as the Hebrew — another of the cousin pairs that recur across this Atlas.
Life-names cluster noticeably in traditions and periods with high infant mortality. They are frequently not descriptions but petitions.