desktop-basefilename

desktop-basefilename is a variable defined in `desktop.el'.
Its value is

".emacs.desktop"

• This variable is an alias for `desktop-base-file-name'.
• This variable is obsolete since 22.1;
  use `desktop-base-file-name' instead.

Documentation:
Name of file for Emacs desktop, excluding the directory part.

You can customize this variable.