In IIS we have a series of accounts an application pool can run under:
- Network Service
- Application Pool Identity
- Custom User
- etc
My question is if I have a site hosted on an Azure App Service do I have the equivalent accounts to choose from?
There's no such a thing. The closest would be managed identity / service principal, where you create an account in your Azure AD and assign it to your application.
More info:
https://learn.microsoft.com/en-us/azure/active-directory/managed-identities-azure-resources/overview