Database
[{"_id":NumberLong(2761632),"data":{"field.with.dots":{}}},{"_id":NumberLong(2761633),"test":{"a":"a","b":"b","c":"c","v0.0.1":"ok"}}]
Query
db.collection.aggregate([{"$match":{$expr:{$ne:[{"$ifNull":["$test",{}]},{}]}}},{"$set":{"test":{"$setField":{"field":"v0.0.1","input":"$test","value":"$$REMOVE"}}}},{"$merge":{"into":"collection","on":"_id"}}])