how to use $addToSet and $inc value of the set item in MongoDB

Try this one:

var newEvent = "e2"
db.collection.aggregate([
   {
      $set: {
         events: {
            $cond: {
               if: { $in: [newEvent, "$events.eventName"] },
               then: {
                  $map: {
                     input: "$events",
                     as: "event",
                     in: { $mergeObjects: ["$$event", { times: { $add: ["$$event.times", 1] } }] }
                  }
               },
               else: { $concatArrays: ["$events", [{ eventName: newEvent, "times": 0 }]] },
            }
         }
      }
   }
])