You will always be the owner of the stocks you purchase. If Robinhood is set up like most (all?) brokerages, then your assets are held in a separate entity that would be unaffected by a bankruptcy. So creditors of Robinhood can't go after your assets, even when they are managed by Robinhood.

Of course, should Robinhood go under, don't expect easy access to your assets, until some other brokerage takes it over.