Rather than modifying the \xxxautorefname macros by hand, I suggest you load the cleveref package (after loading hyperref) and use \cref for lowercase label strings and \Cref for uppercase label strings.
A part of your preamble would look like this:
...
\usepackage[colorlinks]{hyperref}
\usepackage[nameinlink,noabbrev]{cleveref}
...
Next, in the body of the document, perform a global search-and-replace of \autoref with \cref.
In case you're curious: The nameinlink option makes the cross-referencing call-outs produced by \cref look like those produced by \autoref.
For more on cross-referencing packages for LaTeX in general and the hyperref and cleveref packages in particular, see this answer to the posting Cross-reference packages: which to use, which conflict? (Shameless self-citation alert!)
\def\equationautorefname{equation}directly below\usepackage{hyperref}(see https://tex.stackexchange.com/a/137435/). – Marijn Apr 20 '18 at 09:05