If it is a legally separate (own tax ID) company, the gift goes on that record with soft-credit to the individual. The receipt should reflect the name of the company. The donor can work out the filing details.
FWIW, while I have a separate LLC, I file a single tax return (1040) with a separate form within for the LLC. However, my CPA insists that I track my charitable donations distinctly when made by my LLC. It's more of an ease of booking thing.
John
John H. Taylor
919.816.5903 (Cell/Text)
Big Ideas - Small Keyboard