How to creare a second login for a second database in Azure? How to deny a user access to one of the databases?
If you don't want the user to have access to the database at all make sure your user does not have system administrator privileges which would allow them access to every database. Baring that, on the database you don't want the 2nd user to have access to, run the following:

USE [1stDatabase]
DROP USER [2ndUser]
GO


To create an exclusive user for the second database:

USE MASTER
CREATE LOGIN [login_name here] WITH PASSWORD = '[password here]'
GO

USE [2ndDatabase]
CREATE USER [login name here] FOR LOGIN [login name here]
GO