How can I use grep to show just filenames on Linux?

The standard option grep -l (that is a lowercase L) could do this.

From the Unix standard:

-l
    (The letter ell.) Write only the names of files containing selected
    lines to standard output. Pathnames are written once per file searched.
    If the standard input is searched, a pathname of (standard input) will
    be written, in the POSIX locale. In other locales, standard input may be
    replaced by something more appropriate in those locales.

You also do not need -H in this case.