The name "Sannanpuisto" could maybe used as a loc_name for the northern park if as lakofsth suggested "that most residents nearby, and organizations using the park" use that name, but this I leave up to locals to decide. Later on I'll add some descrition & note tags on some of these object to clarify the situation even more and will probably also 
make a OSM diary entry to explain this interesting and complicated situation more widely as it according to me serves as a warning example in how not to name things.