There are 11 spirits in the game, however you'll only bring 9 of them to the Everdoor to pass on.
The 9 Spirits are:
Gwen
Summer
Alice
Astrid
Giovanni
Gustav
Stanley
Bruce & Mickey
Elena
*As pointed out in the comments: A few updates have added in Beverly, Daria and
Jackie who also need to be released.*
Atul will leave on his own after progressing his story quest and his Spirit Flower will appear in his house like normal. Buck will simply remain on your ship forever, so don't worry about sailing around trying to get another quest to pop up for him.