Umbar is stated to be a pre-Númenórean name whose meaning had been forgotten by the late Third Age. It does appear to be at least partly Elvish in form, but any interpretation is necessarily highly speculative.
The name appears to contain the word mbar, 'home' or 'dwelling-place', an element seen fairly frequently in names like 'Brithombar' or 'Eämbar'. The 'u-' prefix is hard to decipher, but it would normally form a negative, so perhaps 'Umbar' simply means 'not home' or 'away from home' (to the Númenóreans or Gondorians, that is). However, there is no definite support for this theory in Tolkien's works.
Umbar is also known to be the Elvish word for 'fate'. This seems an odd source for a placename, and is probably mere coincidence, but it may possibly refer to the fateful landing of Ar-Pharazôn here in the year II 3261, which ultimately led to the Downfall of Númenor.