Milan Dinić

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Image descriptions are stored as content (field <code>post_content</code>) while captions are stored as excerpt (field <code>post_excerpt</code>). This means that descriptions are shown on single attachment pages, while captions are shown in <a href="https://codex.wordpress.org/Gallery_Shortcode" rel="nofollow ugc">galleries</a> and if image is embedded in a post content with a <code>[caption]</code> shortcode.
If you use images just in galleries, in order to have text below image in both places, you need to fill both fields.
This plugin changes that. You only fill description field and that text is used as caption of image in galleries.
There are no options or settings, just enable plugin and everything works automatically.

Descriptions as Captions in Galleries

Show image descriptions as captions in galleries.

wpcocktail

The Site Title Caption Modifier is a simple WordPress plugin that sets the caption of all images in your WordPress site to the site title. This is particularly useful for maintaining a consistent branding or style across all posts and pages. The plugin works by hooking into the WordPress ‘img_caption_shortcode’ filter and modifying the caption output.

Image Caption for WP

Automatically sets the caption of all images to your site's title.

Descriptions as Captions in Galleries vs Image Caption for WP