[{"_id":1,"name":"value1","x":1,"y":2},{"_id":2,"name":"value1","x":2,"y":2},{"_id":3,"name":"value1","z":10},{"_id":4,"name":"value1","z":20},{"_id":5,"name":"value2","x":8,"y":3},{"_id":6,"name":"value2","x":8,"y":3},{"_id":7,"name":"value2","z":15}]

db.collection.aggregate([{$match:{name:"value1"}},{$group:{_id:"$name",x:{"$push":"$x"},y:{"$push":"$y"},z:{"$push":"$z"}}}])