Is it possible to change the port that the azure server uses? I currently only see the ability to add IP addresses that can be used to access the server. Or is it required
Assuming you're referring to SQL Database Service and its associated firewall, no: You may only add IP addresses to the firewall, for access.
There is no ability to change the port that the service listens on. You'll need to allow for outbound traffic on port 1433, if you want to access the database remotely.
Also, just FYI - port 1433 is the standard SQL Server port.
Note: The inability to change the listening port is strictly for the SQL Database service. This restriction doesn't exist for SQL Server running in a VM, since you have total control of inbound ports and related port-mapping via network security groups.