It depends on how you want to define historian. By Webster's Dictionary, which includes being "a student of history" then yes, you qualify.

But, as you are no doubt aware of by now the most important aspects of a historian's trade is conducting research, synthesizing those materials, and engaging in a discussion with others within your area of expertise. These are all things that a BA helps prepare you to do, but usually are not done until you begin studying history at the graduate level (the exception being some upper level research seminars).

In essence it boils down to if you consider being a historian to be derived from your studying history, or from your actively engaging with others in your chosen area of study/expertise.

And of course, your company at the time of saying so. Saying it on a date will net you an entirely different response than in a room full of academics.

Do you have anything published? What do you specialise in?

I've wondered in a similar way about who gets to call themselves a Scientist. In the case of science, is it anyone who has a BS?

My thoughts are that if you are either working towards an advanced degree in the field, have an advanced degree in a field, or are paid for your work in the field you can legitimately describe yourself as part of that field.

So graduate students, PhD holders, and folks working in the field regardless of their highest level of education are can say that they are Scientists/Historians/part of whatever community is being discussed.

So in your case I would say you can't really call yourself a historian unless you are enrolled in grad school or you are working in the field.

I wouldn't call someone with a BS in Biology a scientist unless they met those criteria and I feel the same should apply to History. However, I am not a historian, so would defer to any folks who are actual historians (recognizing the tautological nature of my argument as I would probably only consider them actual historians if they met my criteria).