Slightly more complicated than that, I think; I suspect the part name will need to be edited in the "Manage Parts" Dialogue. But in any case, the manual is the best place to start ...
The name you gave to this thread is your answer. Go to the Finale manual and type in "Part names in linked parts".
Your answer will appear.
Basically you need to use the part/score name insert.
[One of the weaknesses of Linked Parts is that they don't handle new parts (added after the score is created) very well ... in my experience, anyway.]
Gareth J. Green
Fin2011, running under Vista 64-bit
Also under Windows 7 on a Samsung Laptop
"An expert is a person who has made all the mistakes that can be made in a very narrow field." - Niels Bohr (1885 - 1962)