Can I change /themes/ name?

Well, of course you can, but that would prove to be an unwise decision, as it’s built into wordpress…editing core files is strongly discouraged for many reasons.

In terms of updating WP? That’s ok, I can’t do that anyway due to server setup ??

The more important question is, is this a simple name change or do I have to edit other files?

What are you trying to do? Change to a new theme?

Not at all. I’ve got customizations located in my theme’s folder for HTML5 playback, however when people hover over a thumbnail they get the absolute path, i.e. domain.com/wp-content/themes/theme_name/mp4.php

I can live with wp-content, but I’d rather rename “themes” to “core” or something as “themes” in this case makes it sound really naff.

Create a folder off the root, set proper permissions, FTP upload to it and change the links properly. You can also change the uploads folder (this will not affect existing posts/pages) Admin Dashboard>Settings>Media