Database

[{"name":"ahmet"},{"name":"barış"},{"name":"ceyhun"},{"name":"aslan"},{"name":"deniz"}]

Query

db.collection.aggregate([{$group:{_id:{"$substrCP":["$name",0,1]},name:{$push:"$name"}}},{$project:{_id:0,name:{"$arrayElemAt":["$name",{$toInt:{$multiply:[{$rand:{}},{$size:{$ifNull:["$name",[]]}}]}}]}}}])

Result