The landscape for software that helps in adding comments to a website is does not shine so bright. A few big closed source companies, such as Disqus or Facebook offer an API to integrate comments. The problem with these services is that they own all the data and we have no Idea what we expose the website visitor to.
While Wordpress does come with comments baked into the platform, unfortunately Ghost and others do not. This article has a good overview of the problem in Ghost and I would identify myself as the power user, that wants a good product and respects users privacy.
That which is why I kept looking for solutions before seriously considering moving away from Ghost.
Looking at the comments (This is why we do need them) from the above article is where I have found the solution that works for me => Commento.
Available on Gitlab and with pretty good setup documentation, this commenting service allows functionalities similar to Disqus while giving all the benefits of hosting the software on your own server. Of course you can also let the company host this for you, at a really reasonable price, while still being able to see the Codebase it is running on.
If you do care about your users and would like to provide the people that visit your website with privacy and no third party ADs than you should give Commento a try.
Btw, I have no connection to them whatsoever. I just really like their product and would love for others to discover it!