set_theme_mod( string $name, mixed $value )

function set_theme_mod( $name, $value ) {
	$mods = get_theme_mods();
	$old_value = isset( $mods[ $name ] ) ? $mods[ $name ] : false;

	/**
	 * Filters the theme mod value on save.
	 *
	 * The dynamic portion of the hook name, `$name`, refers to the key name of
	 * the modification array. For example, 'header_textcolor', 'header_image',
	 * and so on depending on the theme options.
	 *
	 * @since WP-3.9.0
	 *
	 * @param string $value     The new value of the theme mod.
	 * @param string $old_value The current value of the theme mod.
	 */
	$mods[ $name ] = apply_filters( "pre_set_theme_mod_{$name}", $value, $old_value );

	$theme = get_option( 'stylesheet' );
	update_option( "theme_mods_$theme", $mods );
}