The problem with starting a name with "The" is that dropdowns and other alphabetical lists aren't always consistent how they treat it, and also people look for Baltic and can't find it because they don't know whether to look under 'the' (if you are told to go to "The Baltic" station you can't tell if they mean 'the Baltic station' or 'the The Baltic' station.So anyway, all that waffle aside, "The Baltic" sounds a bit less odd than just "Baltic", but "Liverpool Baltic" not only sounds odd but also breaks Merseyrail's existing naming convention. There are already two other stations starting "The" so it is not ground breaking.
Putting city names in front of station names is confusing unless it is the terminus/main station, particularly if none of them are 'central' or other equivalent which denotes it is the best for the long distance traveler.