So if you give choice parameter the name PROJECT_NAME and the choices to be :-
then, Jenkins will automatically assign one of these value(i.e proj1, proj2, proj3) to variable PROJECT_NAME as per the choice triggered to start the build. You can infact use $PROJECT_NAME as a variable anywhere in the job configuration page.
you can use a build shell to perform your mapping the proj1, proj2 and proj3 to property1, property2 and property3.
if [ $PROJECT_NAME = "proj1" ]
then <your logic goes here for implementing theme1>