I was just reading about the impacts so far today, and ironically, it only mentions impacts in Scotland. 
https://news.sky.com/story/uk-weather-live-updates-travel-disruption-expected-with-wet-and-windy-warnings-in-place-as-uk-braces-for-storm-gerrit-13038118
Storm names are issued when a storm has the potential to warrant an amber warning. Warnings are issued on an impact basis, rather than a 'how high are the winds, how deep is the snow' basis. This means that a windstorm in an isolated area, with sturdy housing, not many people likely to be on the roads etc is less likely to get a warning than the same strength winds would get over say Manchester or London.
So I think had for instance that snow happened over a deeply populated area then it would have recieved an amber warning. (and perhaps it should have done anyway) It does show though that there is a bit of a skill in reading warnings I think. People see yellow warnings and carry on as normal, when actually the event can still be pretty impactful on them.