Not all - but Eb was apparently Blackstaff even before he became Senior Council - he becomes SC during the books, but Kincaid knows him as Blackstaff for a long time. So some outside have to know. And I think the Staff does select
Those in the same field like Kincaid, or the Summer or Winter Knights, or Thomas predecessor as enforcer of the White Court would know as a professional courtesy. They have faced Eb in combat and would therefore know from firsthand experience. Margaret was being groomed by Eb to take on the Blackstaff, and despite being LeFay, ran away from it. Eb was previously Captain of the Wardens so likely took on the Blackstaff then. For some reason he didn’t consider his successor as Captain should have the Blackstaff, and that is interesting. Was Eb still Captain when the Wardens and Senior Council took on Kemmler? If not would he have been there? It was clear he wasn’t Captain when they took Harry in. When did he resign as Captain and why? I think it may have been when Margaret fled to avoid being sent out after her. This may be a reason why Eb refused Senior Council for so long, it avoided him coming into official contact with Margaret unless she clrearly broke the seven laws, which she appears to have skirted. Retaining the Blackstaff mean’t no one else could use it against Margaret.
And no, Mother Winter does not carry a .22 short, she prefers germ warfare. You really don’t want to break into her house and disturb her at night.