The group in subject site setting that might accomplish what you are looking for. When that setting is enabled, the email subject line will, by default, contain the name of the first group in the PM. As an example, here’s the subject line of a PM I sent to my ‘Eurorack’ group to test the setting:
[Simon's Demo] [Eurorack Enthusiasts Club] Testing the subject line for group PMs
The first field in the subject is the name of my site. The second field is the name of the group the message was sent to. The final field is the PMs title. These values are set based on the value of your site’s email subject site setting. The default value of that setting is:
[%{site_name}] %{optional_pm}%{optional_cat}%{topic_title}
That setting’s %{optional_pm} placeholder is what gets set to the group name. If you send a PM to an individual user, with the group in subject setting enabled, that placeholder will be substituted with the text ‘PM’. For example:
[Simon's Demo] [PM] More subject line tests
Let me know if the use of either of these settings is unclear, or if this doesn’t accomplish what you are looking for.