It’s been a while since I used it but as I recall, the calendar has categories of appointments which may be configured to last different lengths of time.
I do not think the appointments can be created in precisely the manner you mention, but you could make a category for ‘clinic 1 Dr x’ and the time that appointment lasts for that Dr. And the categories can be different colors, so making them for each Dr like that, would make the appointment slots the different colors for each Dr. Does that sound like it’d suit?
It sounds like you’ve been working with categories so this info may be redundant:
Here’s the wiki page that shows the configuration:
It is an old set of instructions but the applicable steps still work.
The appointment category would be selected when the appointment is made (first pic below)
This shows the list of currently active categories, which is where you’d see “clinic 1 Dr x”
Category config is found at Administration/ Other/ Calendar, then click the ‘Categories’ link on that page (2nd pic below)
Each category on the appointment list will have its config section here (3d pic below)