You should ask if the brand name and product name create any untrustworth-ness to user perception. If you clarify brand or product name has not any trustworthy issue, you can try to give "reasoning" or "promises" at the context of login form.
"We won't post something to your facebook wall, we promise" - can be nice for facebook social login.
"We don't tweet for advertising" - can be nice for twitter social login.
We need your e-mail(orthodoxy) because (any sensible reason) - This can help to convince user to continue to an action.
Lastly, you can create counter-arguments like if they signed up, why don't they want to log-in? If you are using an username and password of another web application, then you shall show product or company has legal papers for to do business on top of that service.