by adding your parameters to the report header, copying them in Preview mode, and then pasting them to your new report the entire parameter is copied, not just the name.
if you've got parameters from multiple reports:
(a) the other method then is to use an enterprise product (businessobjects enterprise or crystal reports server) and look into business views where you can have parameters as part of the overall foundation.
or
(b) if you don't have that just create a single parameter template report where you copy all of your parameters. it's really not that difficult.