Direct Access connection name renaming?

We have an existing Direct Access implementation which is working fine.  However, we want to rename the DirectAccess connection name to something different.  It looks like it may be able to be done by clicking on Edit under step one under Configuration.  See the attached screenshot.  My question is, will this disrupt any of the client connections, and will the name refresh on the client computers when they look at their DirectAccess client connection status?  Is there potentially a better way to change this connection name?

Thanks!
Capture-DA.JPG