Most people in BC know the BC Liberals are a centre-right not centre-left party.  As for liberal being misnomer it depends.  The BC Liberals are a classical liberal party while the federal Liberals are a social liberal party.  Historically liberalism was about minimal government so more like the BC Liberals however in North America, but not Europe liberal parties in the 60s moved to the left.  Because socialism was a four letter word in North America, but many especially in Canada supported social democratic ideas it was a way to bring about social democratic ideas without the negative name of socialism being hung around it.  Also the federal Liberals are a centrist party and tend to split fairly evenly between BC Liberals and NDP whereas federal Tories go overwhelmingly BC Liberal and federal NDP overwhelmingly NDP.