This is something a lot of people would like, but right now that feature is marked "not planned" by the developers since it would be difficult to implement. That might change if they get more funding / get through more of the backlog / someone else works on it.

You can see those feature requests and discussions on their GitHub page: https://github.com/LemmyNet/lemmy/issues/5110

You can totally send off multiple messages to moderators and see who responds first. I will say though that if it's not urgent, the mod may just be too busy to sit down at a computer and get through those messages.

Personally I look through the profile and see which mods have made a post or comment recently, and message based on that.