Specify completion without name

[Peng Yu]

Hi,

I want to customize the command completion for completing executables,
I want to search in a file (which includes all the executables in
PATH) rather than the default PATH variable. But I don't see how to do
so, as the following help indicates that it can only configure how to
complete the arguments of a command. Does anybody know how to
configure command completion for the name itself rather than its
arguments? Thanks!

~/Downloads$ help complete
complete: complete [-abcdefgjksuv] [-pr] [-o option] [-A action] [-G
globpat] [-W wordlist] [-P prefix] [-S suffix] [-X filterpat] [-F
function] [-C command] [name ...]
    For each NAME, specify how arguments are to be completed.
    If the -p option is supplied, or if no options are supplied, existing
    completion specifications are printed in a way that allows them to be
    reused as input.  The -r option removes a completion specification for
    each NAME, or, if no NAMEs are supplied, all completion specifications.

-- 
Regards,
Peng