I don't think so. Why does it have to be in the Caption? Could it be a separate sheet in a dashboard?
This can be done, though it's pretty rare because we don't have the same precision with formatting captions that we do in a view.
The following will work whether Name is a dimension in the view or not, you can do this with two measures:
- Count of Names: TOTAL(COUNTD([Name])). This table calculation will have an Advanced Compute Using on all the dimensions in the view.
- Name Check: IF [Count of Names] == 1 AND [Name] = "Jane Smith" THEN 'myCaptionTextHere' END
Put the Name Check field on the Level of Detail, then add it to your caption.
At least in Tableau 8.1, it has to be separate fields because of the way TOTAL() is computed, that might have changed in 8.2.