Can I have an additional functions.php file in WordPress?

You can get rid of the theme update situation by using a child theme. Your child theme will work as an extension of the parent theme that you update often. You can learn more about child theme from here.

But if you don’t wanna use child theme then yes, you can add as many additional functions file as you want. A regular include or require will just work fine. You can include file using a relative path or you can use get_template_directory() function for an absolute path. For instance

include get_template_directory() . '/inc/functions-1.php'; // if it's inside inc directory
include get_template_directory() . '/functions-1.php'; // Or if it's not inside any directory