A workspace, according to the VSTS help "Represents a client-side copy of the files in the repository that you want to work in." What that means is that the TFS server needs to know where to put the files on your local drive when you perform a Get operation; and you have to specify it, there are no defaults and the server will not guess the location. Notice that I said 'server', this information is tracked on the server.

Since workspace point to computer name, changing computer name on local PC will impact to workspace setting. 

Computer name value can't be change from the client software. The dialog was disabled on computer name as shown in picture below.

To change computer name in workspace setting, connect to TFS database (contact TFS administrator to do this if you are not an administrator). Please follow this steps:

• Open TfsVersionControl database.
• Execute query below to make sure workspace which to be updated.
  

  SELECT * FROM tbl_Workspace
  WHERE WorkspaceName='AMASYKUR'

  
  The result might be like picture below
  
• Update Computer field to new computer name.
  

UPDATE tbl_Workspace
SET computer='NEWCOMPUTER'
WHERE WorkspaceName='AMASYKUR'

I hope this trick is useful

Disclaimer : please be very careful when conducting this procedure. I am not responsible if your TFS data is messed up