You can't switch the user account in SharePoint Designer 2013
Original KB number: 2738178
Summary
This article describes how to start Microsoft SharePoint Designer 2013 as another SharePoint user.
Method 1
Start the Spedesign.exe process by using a different user account. To do so, follow these steps:
Go to the SharePoint Designer 2013 installation folder. By default, the folder is installed in one of the following locations:
C:\Program Files\Microsoft Office\Office15
C:\Program Files (x86)\Microsoft Office\Office15
Press and hold the Shift key, right-click Spedesign.exe, and then select Run as different user.
Type the credential of the user, and then click OK.
Method 2
Log on to Windows by using another user account, and then run SharePoint Designer 2013.