Music library file cannot be saved. A duplicate file name was specified

I purchased A new Mac mini and installed my older computer files to it. Still have the old one. Since it was from the old computer it saves under the same library name on my new mini, it's been fine for a couple of months now I notice the above notice. I'm not sure how to handle this. I definitely want all my music on my new mini as the older laptop is a 2019 MacBook Pro with Intel. How do I save all my music on the Mini and change the Library name? I've got a huge library and don't want to make a mistake and lose everything. Please can someone advise me how to proceed. If I can keep my music on both it would be great but afraid if I try to rename the music library on the mini I will lose everything. I only have purchased music, mostly Apple but also from CD's and other purchased mp3's from many years ago.