We study the problem of hiring a team of selfish agents to perform a task. Each agent is assumed to own one or more elements of a set system, and the auctioneer is trying to purchase a feasible solution by conducting an auction. Our goal is to design auctions that are truthful and false-name-proof, meaning that it is in the agents' best interest to reveal ownership of all elements (which may not be known to the auctioneer a priori) as well as their true incurred costs.We first propose and analyze a false-name-proof mechanism for the special cases where each agent owns only one element in reality. We prove that its frugality ratio is bounded by n2n, which nearly matches a lower bound of Ω(2n) for all false-name-proof mechanisms in this scenario. We then propose a second mechanism. It requires the auctioneer to choose a reserve cost a priori, and thus does not always purchase a solution. In return, it is false-name-proof even when agents own multiple elements. We experimentally evaluate the payment (as well as social surplus) of the second mechanism through simulation.