What is the nickname given to left-handed people?

It depends which way you are using it.

If you are saying left as in "They left me" another Word for left would be 'abandoned' or 'deserted.'

If you are saying left as in "I turned left" then it is the antonym of right.

If you say "they have all left", apart from it being incorrect grammar, another Word would be 'gone' or 'departed'.