Hey @votsiosh,
Thanks for the screenshot ??
I’ve performed some cross-testing for us today on several of my sites which have the latest versions of WordPress, WooCommerce and our free Storefront theme as the only enabled software. When doing so I’ve not been able to replicate the behaviour which you describe with the Order Received email being sent for Completed Orders.
On my test installations, I changed the status of an order from Processing to Completed and the correct email was sent by both of my installations. Below is an animated screenshot of the Completed order email being sent upon updating the order status to completed.
Image Link: https://cloudup.com/cqaMpX6j88x
From what you have described, it could be code from another plugin or theme which has caused a possible conflict and affected the functionality of WooCommerce.
To see if that is the case we’d suggest carrying out a conflict test on your site by disabling all other plugins aside from WooCommerce along with switching to a theme like Storefront. This will help with trying to and locate what software you have installed which could possibly be causing this behaviour? You could use a free plugin called Health Check and Troubleshooting to carry out such testing.
When in Troubleshooting mode all plugins will be deactivated and only the admin of the site carrying out the troubleshooting would see those changes. Any customers visiting the site would see no changes at all.
Once you have disabled all other plugins and switched theme if the behaviour is resolved you can then enabled your theme and sites plugins testing after each one is enabled until the behaviour returns to locate the culprit.
https://docs.woocommerce.com/document/how-to-test-for-conflicts/