I've done everything that you've suggested, (Which is how I'd done previously) and it STILL refuses to change to the new file name in the assembly browser. However, It does this on ALL downloaded third party files, not just the Schunk files. There is obviously a setting on my PC/Software which prevents me from changing the parameters as discussed.
I'm just going to have to live with it.
Many thanks to you Paul, and everyone else who's contributed.
I'm just going to sit in a darkened room now............quitely!!
As a workaround, would making them each a derived part solve the problem? (Experts far more advanced than I could confirm. I'm taking a wild-ish stab here.)