How to identify BBS without the number tag

Are you doing this to rebuild for use or just because you want to know what you have? I dont know of a way to identify the carbs without a tag, but I will share my experience from my carter bbs rebuild this week. I have two bbs's sitting on my bench with tags that identify them as the models that I may want to use. I open both the carbs to find that one of the carbs internals DO NOT match what the tag number says its supposed to be. So, I used the factory service manual to find the specs of the particular carb that I was looking to install on my vehicle. The manual includes the Carter tag numbers and detailed descriptions of that particular carb. From what I could tell, the bbs can be very easily custom built because the throttle plate, bowl assembly, and horn (top) are all independent and can be interchanged without too much modification.
So, I went through both of my carbs to find the main jet and step up wire I need for my application. Then I used the FSM to confirm the measurements for the horn and venturi. This ensures that I am using the correct casting number and there will be a proper amount of air/fuel flow for the application. Use the FSM to confirm float level, adjustments, and main metering jet numbers and step up wire diameters. The idle orifice and accelerator pump jet do not seem to be custom items. (Main metering jet, step up wires, idle orifice, and a couple of other pieces are almost impossible to find or can only be found NOS, so don't lose, or break them)
So if you know what you are looking to accomplish, I believe you could take the measurements and custom build the bbs the way it needs to be for your application without the tags.