So the names are still correct on the original source drive, but have changed to numbers on the destination drive? Then try transferring the files again, perhaps using a different method.
How were the files being transferred? Manually copying them using the Finder? Using the command line, if so provide the command(s) used? Or using a third party app...if so, which app?
Was this transfer between two external drives? Or from an internal drive to an external drive? Or from an internal drive of one computer to an internal drive of another computer? Was file sharing involved between the two computers? Was an intermediary drive used to perform the transfer between the two systems (USB stick or drive)? Details in how the computers were connected and how the transfer was done may be important as well.
What version of macOS is on each computer?
We definitely need more precise details to try to figure out what may have occurred here. If the source files on the original computer are still intact and correct, then at least you have options available. I was afraid you meant the original files on the source drive had their names changed.