I notice that 'Liverpool Baltic' now appears on the line diagram on the Northern line platforms at Central. That could be encouraging, if slightly confusing because work seems nowhere near starting.
I wonder how long the station name will survive. 'Liverpool Central' makes sense to distinguish it from Birkenhead Central, and to identify the main Merseyrail station in the city. 'Liverpool Lime Street' is of course the main terminus for passengers elsewhere in the country, but 'Lime Street' alone is used on the Wirral line. Moorfields or James Street don't usually get the 'Liverpool' prefix. So why should Baltic? Some countries (eg Italy) make a point of prefixing the city name to the individual station name, for all stations within the city limits. British custom has never been to do that, otherwise we'd have Liverpool Sandhills, Liverpool Kirkdale, Sefton Bootle Oriel Road (!), Knowsley Kirkby etc. If Merseyrail becomes (officially or otherwise) distinct from the national network there would be even less justification for it.