You require a tool that can delete the .hhs filename suffix from the filename. find can not do this for you, so you will have to call another utility through -exec:

find "$HOME" -type f -name '*.hhs' -exec sh -c '
    for pathname do
        mv -i "$pathname" "${pathname%.hhs}"
    done' sh {} +

I'm not using basename here as that would also remove the directory path from the found pathnames (which could be inserted again with dirname, but it would yield messy code).

Instead, I call an in-line shell script with as many found pathnames as possible, and let the script loop over these, renaming the individual files. The new name is constructed using a standard parameter substitution that deletes the string .hhs from the end of the value of $pathname.

Related:

• Understanding the -exec option of `find`

You require a tool that can delete the .hhs filename suffix from the filename. find can not do this for you, so you will have to call another utility through -exec:

find "$HOME" -type f -name '*.hhs' -exec sh -c '
    for pathname do
        cp -i "$pathname" "${pathname%.hhs}"
    done' sh {} +

I'm not using basename here as that would also remove the directory path from the found pathnames (which could be inserted again with dirname, but it would yield messy code).

Instead, I call an in-line shell script with as many found pathnames as possible, and let the script loop over these, copying the individual files. The new name is constructed using a standard parameter substitution that deletes the string .hhs from the end of the value of $pathname.

Related:

• Understanding the -exec option of `find`