How do you extend the Site model in django?

If you only want to change behaviour of the object, but not add any new fields, you should consider using a "proxy model" (new in Django 1.1). You can add extra Python methods to existing models, and more:

This is what proxy model inheritance is for: creating a proxy for the original model. You can create, delete and update instances of the proxy model and all the data will be saved as if you were using the original (non-proxied) model. The difference is that you can change things like the default model ordering or the default manager in the proxy, without having to alter the original.

Read more in the documentation.

I just used my own subclass of Site and created a custom admin for it.

Basically, when you subclass a model in django it creates FK pointing to parent model and allows to access parent model's fields transparently- the same way you'd access parent class attributes in pyhon. Built in admin won't suffer in any way, but you'll have to un-register Sites ModelAdmin and register your own ModelAdmin.

As of Django 2.2 there still no simple straight way to extend Site as can be done for User. Best way to do it now is to create new entity and put parameters there. This is the only way if you want to leverage existing sites support.

class SiteProfile(models.Model):
    title = models.TextField()
    site = models.OneToOneField(Site, on_delete=models.CASCADE)

You will have to create admin for SiteProfile. Then add some SiteProfile records with linked Site. Now you can use site.siteprofile.title anywhere where you have access to current site from model.

You can have another model like SiteProfile which has a OneToOne relation with Site.