Joseph:

The name "Carlos de Godoy" in Western Mexico is what is called a composed name. There were clearly people with this name as early as the late 1500s in Sinaloa and the Juan Carlos de Godoy who is the progenitor of the surnames Carlos and Godoy in Jerez was likely related to these earlier Carlos de Godoys from Sinaloa, though those of us looking into this have no definitely proof.

The name Carlos de Godoy was likely composed in Mexico as there do not appear to be any early passenger records of anybody with this name, but there were a number of Godoys among the early settlers and conquistadores of Nueva Galicia. In that early time, the standard surname custom used in Mexico today (paternal surname followed by maternal surname) was in no way a convention. Often children would take the mother's surname, often the father's and even sometimes a grandparent's name not used by either of their parents. Depended on many factors, i.e. importance of mother's family vs. father's family, need to propogate a name in a family, namesakes, i.e. a child being named for a grandparent (including the surname).

In some cases, where both parents' families were important, a name would become composed with both parents names being used, which is likely what happened in this case. Often the names were written simply as Carlos because priests unfamiliar with the full name dropped the second half. The IGI and VRI databases online often have incorrect or incomplete transcriptions where the transcriber leaves out part of the surname (perhaps assuming it is a maternal surname).

Later, (particularly after Independence) such composed surnames were very much associated with Spanish families which had become persona non grata and so people dropped parts of their surnames to "normalize" them and perhaps be less conspicous, so some Carlos de Godoy became Carlos and some became Godoy.

Do you have any idea as to the location where Eugenio was born or what year he and Michaela Garcia were married?