Outlook 2016 with Gmail keep getting prompted for "Sign in with your Google account" IMAP

Outlook 2016 loads up with a Google Gmail or Googlemail account configured and imediately prompts with a Sign in with your Google account prompt. It happens as soon as the Send/Receive runs to download new messages.

You might see error 0x800CCC0E Outlook cannot synchonize subscribed folders.

If you login, it prompts to authorise Microsoft, which you can do. It just doesn't seem to retain that setting and keeps prompting. Everything looks ok and correctly authorised if you look at https://myaccount.google.com/security

The account is an auto setup from the Outlook 2016 email wizard when you Add Account, which configures IMAP with servers imap.gmail.com and outgoing as smtp.gmail.com

In fact the same setup worked perfectly on another computer. Recreating the profile, the account, checking OST, etc would not fix the problem.

In the end, the fix was found to be related to the account having previously been a @googlemail.com account. If you manually change the servers to be:
   *      Incoming server:  imap.googlemail.com
   *      Outgoing server:  smtp.googlemail.com

the problem is fixed and your Gmail in Outlook will work normally.

'sent on behalf of' user@gmail.com with own domain name - stop gmail doing that

Just set up a couple of gmail accounts for friends' kids and registered their own domains for them. You can easily add the new email address to gmail so it uses their own domain (eg kid@kidsname.com) instead of a generic gmail.com one (look under Gmail Settings > Accounts & Import > Send As)

However using the standard setup which specifies using Gmail's own SMTP server to send mail out, the message arrives in Outlook with a 'sent from user@gmail.com on behalf of kid@kidsname.com. Looks a bit messy and gives away the gmail username.

You can stop that sent on behalf of from appearing by changing the Gmail settings slightly. Go back into the Send As setting mentioned above then click Edit info for the own domain name entry (kid@kidsname.com).

Specify that you want to use the domain's own SMTP but delete the smtp.kidsname.com entry and change to smtp.gmail.com (yes yes, same server as before, but it doesn't add that sent on behalf of label sent like this). Use the user@gmail.com login and password, specify TLS and port 587.