How to set the WordPress logo programmatically with PHP

The logo is a theme mod, so you can set it with set_theme_mod( 'custom_logo', $value );, but the value needs to be an attachment ID, so you’ll need to upload it first.

If you don’t want to upload anything, you can use the get_custom_logo() filter to provide your own HTML for the logo. If you want to mimic the way WordPress does it, just make sure to include the link custom-logo classes:

function wpse_304465_custom_logo( $html ) {
    if ( $html == '' ) {
        $html = sprintf( 
            '<a href="https://wordpress.stackexchange.com/questions/304465/%1$s" class="custom-logo-link" rel="home" itemprop="url">%2$s</a>',
            esc_url( home_url( "https://wordpress.stackexchange.com/" ) ),
            '<img src="http://www.example.com/myimage.png" class="custom-logo" itemprop="logo">'
        );
    }

    return $html;
}
add_filter( 'get_custom_logo', 'wpse_304465_custom_logo' );