for sharing the genus name part we have 2 options:

A) consistent dwc approach:
We keep the dwc:genus definition as it is to be inline with the other classification terms including subgenus. All of these should contain the accepted classification, not necessarily the part of the name. 
Two new terms genericName and infragenericEpithet are then proposed to hold the genus part of a name and the infra generic part. This approach keeps the dwc terms consistent and does not mix classification terms with terms for atomized names.

B) least change approach:
Taking into account that many people already use dwc:genus for the name part we alter the definition of the term as proposed here. This results in the least impact on existing publishers and probably consumers too. But it has the drawback of i) dwc terms are inconsistent with family & subgenus being the classification, not the name part, ii) no option anymore to share the genus classification, iii) no way to share all infra generic names

I would hope we can start a vote around those 2 options with A) being my clear favorite