The class of Groves mechanisms has been attracting much attention in mechanism design literature due to two attractive characteristics: utilitarian efficiency (also called social welfare maximization) and dominant strategy incentive compatibility. However, when strategic agents can create multiple fake identities and reveal more than one preference under them, a refined characteristic called false-name-proofness is required. Utilitarian efficiency and false-name-proofness are incompatible in combinatorial auctions, if we also have individual rationality as a desired condition. However, although individual rationality is strongly desirable, if participation is mandatory due to social norms or reputations, a mechanism without individual rationality can be sustained. In this paper we investigate the relationship between utilitarian efficiency and false-name-proofness in a social choice environment with monetary transfers. We show that in our modelization no mechanism simultaneously satisfies utilitarian efficiency, false-name-proofness, and individual rationality. Considering this fact, we ignore individual rationality and design various mechanisms that simultaneously satisfy the other two properties. We also compare our different mechanisms in terms of the distance to individual rationality. Finally we illustrate our mechanisms on a facility location problem.