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.

Terry Chay

The core <a href="https://developer.wordpress.org/reference/functions/img_caption_shortcode/#source-code" rel="nofollow ugc"><code>img_caption_shortcode()</code></a> function <a href="https://core.trac.wordpress.org/ticket/24990#comment:13" rel="nofollow ugc">doesn’t process shortcodes when they’re in the caption (just when they’re in the image)</a>. This simple plugin changes it so that captions can contain shortcodes.
It also fixes some other small edge-case bugs in the original code.

Nested image caption shortcode

Allows caption shortcode to have shortcodes

Image Caption for WP vs Nested image caption shortcode