The phrase "to attract big names" means to bring in or secure the participation of well-known, prominent individuals or organizations. It can refer to a variety of situations, such as attracting high-profile speakers or performers to an event, securing the support of influential people for a cause or campaign, or attracting major corporations as clients for a business. The goal is to have the association or endorsement of these well-known figures or organizations bring additional prestige, credibility, or attention to the endeavor.