If you wish to stop analysis and remove your project from Codacy, you can find the option under your project Settings tab.
This will not remove your project from your VCS host. It will only remove data concerning your project in Codacy.
On this page, you can also transfer your project to another of your organizations.
I renamed my project on GitHub/Bitbucket
There's no need to remove your project. You can update the project URL to point to the new location. This way you won't lose historical data about your project.