I believe pinking shears are from an unrelated verb, meaning prick or pick (holes in...).

There is an old tailory firm in London called Thomas (?) Pink, but another idea I've heard is that only the Sovereign was allowed to use red (= "scarlet") livery, so others had to use a different colour. (We're talking heraldic colours here, where there are no fine distinctions.) But I can't vouch for either of these.