Only allow one shortcode in post content

functions.php

add_filter( 'the_content', 'MyTheme_do_first_shortcode' );

function MyTheme_do_first_shortcode( $content ) {

	// EDIT: Shortcode name (without brackets)
	$shortcode = 'shortcode-name';

	if ( has_shortcode( $content, $shortcode ) ) {
		$regex = get_shortcode_regex( array( $shortcode ) );
		$i     = 0;

		$content = preg_replace_callback( "/$regex/", function( $m ) use( &$i ) {
				return MyTheme_do_shortcode_tag( $m, $i++ );
			}, $content );
	}

	return $content;
}


function MyTheme_do_shortcode_tag( $m, $i ) {
	global $shortcode_tags;

	// allow [[foo]] syntax for escaping a tag
	if ( $m[1] == '[' && $m[6] == ']' ) {
		return substr( $m[0], 1, -1 );
	}

	$tag = $m[2];
	$attr = shortcode_parse_atts( $m[3] );

	// Don't do shortcode if the index is above 0
	if ( $i ) {
		return '';
	}

	if ( ! is_callable( $shortcode_tags[ $tag ] ) ) {
		/* translators: %s: shortcode tag */
		$message = sprintf( __( 'Attempting to parse a shortcode without a valid callback: %s' ), $tag );
		_doing_it_wrong( __FUNCTION__, $message, '4.3.0' );
		return $m[0];
	}

	if ( isset( $m[5] ) ) {
		// enclosing tag - extra parameter
		return $m[1] . call_user_func( $shortcode_tags[$tag], $attr, $m[5], $tag ) . $m[6];
	} else {
		// self-closing tag
		return $m[1] . call_user_func( $shortcode_tags[$tag], $attr, null,  $tag ) . $m[6];
	}
}

Edit the shortcode name in line 6