You are right in indicating that the name "Brill" seems to suggest the adjective "brilliant." My own thoughts on this matter is that the name that Mansfield gives to her protagonist reinforces the essential divide that exists between Miss Brill's own perception of her life and the reality of it. There is therefore immense irony in giving Miss Brill a name that suggests the adjective brilliant, as it is obvious to the reader that her life is anything but.