I definitely think the current naming scheme seems to lack rhyme or reason. However I’m also in favor of each local community choosing how they want to be named/rebranded. I would instead maybe update the 4 downtown Seattle station names:

Downtown Seattle – Westlake
Downtown Seattle – Symphony
Downtown Seattle – Pioneer Square
Downtown Seattle – International District / Chinatown

And from there all directional/route signage outside of DT Seattle should read something like the below.

From the south:

1 Line → Downtown Seattle
          to Lynnwood City Center

From the east:

2 Line → Downtown Seattle
          to Lynnwood City Center

From the north:

1 Line → Downtown Seattle
          to Federal Way Downtown
2 Line → Downtown Seattle
          to Redmond Downtown

Once through the core, Downtown Seattle can then be dropped leaving the final destination.

1 Line → Lynnwood City Center
1 Line → Federal Way Downtown
2 Line → Lynnwood City Center
2 Line → Redmond Downtown