You can store and interact with git repositories wherever you wish, but there're some platforms availible that add handy features like issue reporting, wikis, easy code browsing, etc.
Gitea (Git + tea, apparantly) is a self-host Git thing like Gitlab, but it is less demanding on server/host resources. Supposed to be able to run on a RaspberryPi, so within 1GB of RAM). Interface is verry Githubby.
The most popular, but centralised.
Gitlab is somewhat like Github, but you can self-host it. They are working towards making these individual gitlab setups federate too, or at least be able to intermingle a bit, using Wikipedia:ActivityPub which is cool!