You know, I wondered that myself when I first noticed the coincidence. But it’s just a coincidence.
The name of the city Ur in the Bible apparently comes from Hebrew ur meaning ‘town, village’. Note that in the Sumerian language uru also means ‘town, village’. The Hebrew word probably was not borrowed from the Sumerian since it has cognates in other Semitic languages. The resemblance is either a coincidence or a trace of an earlier, lost connection between Sumerian and Semitic. Not only that, the Dravidian languages show a remarkable coincidence. The Tamil word for village is ur and the Telugu word for village is uru. The Nostratic hypothesis proposes that there was a prehistoric macrofamily connecting several different language families, including Semitic and Dravidian. Or it my be just a coincidence, or there may have been loanwords traveling between the early Mesopotamian and Indus Valley civilizations.
The German prefix ur- meaning ‘original’ comes from Proto-Indo-European *ud- meaning ‘out, off, away, up’. The same root produced Sanskrit ud- ‘out, up’, Irish úd ‘beginning’, and English out, utter, utmost. The meaning of ‘origin’ comes from the idea of moving out, away from. In phonetics, the sound of -d following a vowel can often change into -r.