Database
[{timestamp:ISODate("2022-06-22T00:00:00Z"),name:"Max",age:20},{timestamp:ISODate("2022-06-22T00:00:00Z"),name:"Brian",age:21}]
Query
db.collection.aggregate([{$group:{_id:{bins:{$dateTrunc:{date:"$timestamp",unit:"week",binSize:1}}},"NamesWithAge20":{$addToSet:{$cond:{if:{$eq:["$age",20]},then:"$name",else:"$$REMOVE"}}}}}])