The acronym "UNIT" had stood for "United Nations Intelligence Taskforce" for over 35 years by the time RTD-Who made it's appearance. To request the change after such a long time seems petty.
I agree. While I understand why they asked for the change, I'd simply drop the whole UNIT reference altogether and replace it with another organisation. It's been 16 years since the old series so it's conceivable the "old ways don't work anymore" ala James Bond.