This is what you have to do to filter by other properties than the ones your model has:
Make new "property" (required)
mark as "safe" in 'on'=>'search' scenario in rules method (required)
set name in attributeLabels method (optional)
add condition with "with" and "together" in search function (required)
set "name" in "columns" as the "property" name(required)
Based on this EXCELLENT post by Piotr Osipa.