If you need to change the folder or theme name for WordPress you need to make the modification to the local folder as well as to the database.

Change WordPress theme folder name:

../wordpress/wp-content/themes/old-name

to:

../wordpress/wp-content/themes/new-name

Change WordPress theme database settings:

The changes are to be made within the wp_options table.

option_name = theme_mods_

theme_mods_old-theme

to:

theme_mods_new-theme

option_name = template

Change option value:

old-theme

to:

new-theme

option_name = stylesheet

Change option value:

old-theme

to:

new-theme

If you have SiteOrigin Custom CSS plugin installed, also change the following:

siteorigin_custom_css

siteorigin_custom_css[old-theme]

to:

siteorigin_custom_css[new-theme]

siteorigin_custom_css_revisions

siteorigin_custom_css_revisions[old-theme]

to:

siteorigin_custom_css_revisions[new-theme]

You may find _transient options but these are only temporary and used by WordPress as a cache effectively and do not need to be updated as they will automatically regenerate.