I'd have no issues calling it M1... the M1 happened years ago and exists now only in the memories of a few enthusiasts... the main bulk of prospective M1 owners wouldn't even have heard of the original M1.
As far as the car itself is concerned, I hear all the 'they should build a lighter version with a tuned 4cyl', but this isn't a realistic thing to expect... modern cars are heavy for a reason... we all want a decent level of build quality and high level of safety. These things cannot be engineered out as they are part of the bottom-up design and build process. The equipment that makes a car convienient for us in day to day driving isn't that heavy as a percentage of the car's weight so there isn't a huge amount of weight BMW could cut out of the car... maybe no electric seats, no leather, but things like electric windows and AC aren't that heavy.
And whilst the current 135i might have similar straight line performance to the TT-RS and base Caymen, it doesn't have the same level of cornering ability... that's the thing that an M version should really address.
If the M1/135iM (or whatever) has around 350bhp, weighs <1,500kg and costs c.£35,000 without extras, I think there would be a big market for it in the UK.