Personally, I think our name is Sarah is not unacceptable, though it sounds strange based on the infrequency of such an answer. The truth of the matter is that grammatically, they only have one name between them: It is a singular subject.
- Our horse's name is Grimm.
- Our address is 615 Gramercy Park Drive.
- Our son is fifteen.
- Our cheesecake is the one covered in chocolate swirls.
In these examples, two people share the relationship with the subject, but the subject is singular.
I think if there were only 10 names to choose from, our name is would quickly become standard, as no one wants to say I'm named Sarah, and so is she several times a week for her entire life.
If the subject is plural, then it needs to follow its proper grammar rules:
- We are both named Sarah.
- Our horses' names are Grimm and Reaper. The Black one is Grimm, and the brown one is Reaper.
- Our sons are 15 and 18.
- Our addresses are different, as we have separated.
If there were only 20 names to choose from in the world, I'm sure the construction would be quite common and acceptable.