parsing in the menu id into theme_mods_themename

You can use set_theme_mod() to save a value in the theme_mod serialized array. Then retrieve it with get_theme_mod().

You shouldn’t attempt to parse a serialized array anyway. PHP has functions to unserialize and seriallize data arrays. You could then access the values through the resulting associative array. But by using the above functions, WP does the serialization and array access for you, you merely set and get individual values.