[{"_id":1,property:true,},{"_id":2,firstDate:"First date"},{"_id":3,lastDate:"Last name"},{"_id":4,date:"date"},{"_id":5,property:true},{"_id":6,name:"Name"}]

db.collection.aggregate([{$addFields:{keysAndValues:{$objectToArray:"$$ROOT",}}},{$match:{"keysAndValues.k":{$regex:"date",$options:"i",}}},{$unset:"keysAndValues"}])