Should you commission a new name as well as the visual identity?
No, if the current name is the one people say when they arrange to meet and it fits on the sign. Yes, only when that name no longer says what you are or cannot be used on the door.
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Ask five guests what they call you, without showing them options. A name nobody can pronounce is launched and the old one stays in the reviews. Either the existing name closed into the mark, or a short list of names that can be said out loud.