The reason that British Columbia is called thusly is due to the fact it used to legitimately be part of Spanish Colombia. Well, sort of. The whole West Coast was claimed by Spain, due to explorers like Juan de Fuca sailing around the area. But it never got settled by the Spanish and the British eventually made their way there overland and it became Columbia District.
But this area didn't really have modern borders until 1848 when the Brits ceded Oregon, Washington and Idaho to the US and created the current border. This area of Columbia District later became known as Oregon Territory after transfer to the US.
So after a fashion it sort of is "annexed Canadians", except Canada as a country didn't exist for another 19 years (and British Columbia didn't join Canada for another four years after that).
There is a modern movement, not particularly popular or practical, to combine BC with the US coastal provinces to create a new country called Cascadia. But it's mostly geography nerds jerking each other off.
But in all seriousness it's because the state was divided during the Civil War and the original Virginia kept on being Virginia. And West Virginia was evidently the most satisfactory name they could come up with for the new state. Could have also gone with North Virginia, but with the context of the civil war (north vs south) they may have avoided that one.