Not as a client.  If you used the taxpayer's name and email address to set up the client, that's what will show even if you change the order on the return.

You can change the return name to include both names if you'd like.

As for the email address associated with a client, it turns out that even if you update it in the Client, it won't change the login associated with that client's account.  It will only change the email address to which Link will send any email.  I highlighted that to Intuit in the FB group but have yet to receive any response.