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.
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