A barmeter would be something to measure a bar with, or perhaps a meter to measure how much alcohol the bar dispenses.
A barometer measures air pressure.
it measures in Bares
there must be vacuum in the Mercury barometer because if air enters the tube the barmeter would become faulty as air pressure will change.
A near vacuum is necessary in the tube of a mercury barometer to isolate the mercury from atmospheric pressure fluctuations. This allows the mercury to accurately reflect changes in pressure without external interference.
Pressure in these things is measured by how tall a column of liquid it can support. Now atmospheric pressure can support many feet of oil, for example, and who wants a barmeter that tall? Mercury is very dense so you can get away with less than a metre high. Problem solved.