Under current legislation, I believe that all number plates now have to show the supplying dealer or retailer (e.g. Halfords) who made up the plates. That being said, if you put a sticker over the dealers name I thinks it’s highly unlikely you would ever be pulled over for it, given that thousands of people seem to drive around with illegal personalised plates (incorrectly spaced to look like a name or whatever) and seem to get away with it (although technically I think it’s an MOT failure if you do so).
However, I’m not sure what you would achieve. A jealous ex is surely more likely to resent the fact that you have a brand new BMW (or whatever marque it is), a fact that you can’t hide, rather than be bothered about which specific dealer it came from?