The inbreeding coefficient estimated by the isonymy method is often much larger than the average inbreeding coefficient (FD). One reason commonly stated is that the surnames are polyphyletic in origin in such cases. The purpose of this paper is to examine the relationship between the inbreeding calculated from isonymy and the average inbreeding coefficient. It was found that when the level of inbreeding is low, especially when the random isonymy (Pr) is much larger than FD, or when the number of surnames is small (which results in a larger value of Pr), isonymy tends to grossly overestimate FD. A small number of surnames per se (not necessarily due to polyphyletic origin of surnames) will be likely to result in an unduly high estimate of inbreeding. The equations established are illustrated by numerical examples.