How to restore mysql DB from only myi files? Our server's hdds crashed and we didn't have a current backup, so we sent our hdds to a data recovery company. They have been working on the hdds for over a week and they have finally managed to save some files from the hdds.

My problem is the saved files are only myi files and they are named numerically, so I don't know which one belongs to which mysql table. Is it possible to recreate myd and frm files from a myi file? Or is there anything else I can do to get current data from myi?
No, it's not possible - you need the MYD file, too.  The MYI file is only the indexes and does not contain any data.  It is like trying to restore the contents of the book High Performance MySQL from only the index pages.