While it is understandable that the term “umbrella” can be seen as overarching coverage this is not the case.
Umbrella is a term used specifically for adding additional limits to a General Liability or Workers Compensation policy (which offers coverage primarily for physical bodily injury to third parties or employees respectively).
That said, extra coverage is always available for other policies outside of General Liability or Workers' Compensation such as Cyber Liability, Errors & Omissions, or Directors & Officers. Extra coverage for these types of policies is generally called “Excess” as opposed to Umbrella.
Excess and Umbrella serve the same purpose (adding additional limits on top of primary coverage) but a General Liability or Workers Compensation policy simply calls it Umbrella other policies call it Excess.