IMAP in Apple Mail with Gmail - problem

I have just set up IMAP within Applemail. I used to have a GMAIL account linked to the Appple mail but have since deleted this connection within GMAIL and disabled IMAP there to. I cannot delete the GMAIL tab as per the screen shot. Maybe Im missing something here.. ??

 

the only account i have is the Applemail. No gmail, but perhaps i will try deleting and re adding this account as see if it solves the problem..

Update: I deleted the accoun, then added it, but again, gmail appears and cannot be deleted.

It transpires, that Apple mail has automatically given the name GMAIL wrongly, confusing things greatly.
I checked the tabs against my online mail server and sure enough they are the same, which exaplins why i couldnt delete the tab. I have now renamed the tab to the correct Email provider..

But i cannot rename the tab in Apple mail - it says cannot be renamed as per screen shot, then reverts back to calling itself GMAIL



Ok, I think it means my ISP Virgin media (UK) is being hosted or using GMAIL hence this confusion, and Apple mail refusing to rename the tab.. Some google searching suggests they using GMAIL.