As of NextGen Designer 12.5, the login screen allows for changing the customer. 

See the Login screen below, "Choose a different customer":

Update the "Customer" and click "Next".

Also, the URL formats with the Customer Name set below will work for all versions of NextGen Designer.

Initially while logging into NextGen Designer (NGD), the Customer name is entered along with a username and password. After logging in, the Customer name is displayed in the top right corner. After logging out, the Customer name field is not displayed on the log in screen for NGD. 

To change the Customer name for NGD, use the following URL format to define a specific Customer:

https://[server name]/mad/index.html#!login?cust=[Customer Name]

by replacing [server name] with your server name and [Customer Name] with the Customer name. 

E.g.

https://demo.micorp.io/mad/index.html#!login?cust=Example

where "demo.micorp.io" is the name of the server and "Example" is the Customer name.