When the both parts are really separeted, you can go to edit mode, select a vertex of one part, press CTRL-L to select all linked verticies. Now you can press P and "selection" to separate this part from the object. You can also use the P-key and separate the objects by "loose parts".
This can only be done if you apply the boolean operation first.
liebe Grüße
Minihawk
*** In Wirklichkeit ist die Realität ganz anders ***