In either ArcCatalog or ArcMap, connect as a geodatabase administrator. Right-click on your connections, go to Administration | Administer Geodatabase, then go to the Connections tab. Here, you will see a list of all current connections to your geodatabase. Your current connection will be the one listed in greyed-out italics:

Connected users can also be shown in ArcGIS Pro. Right click the database connection, click Properties, expand Connections and then select Show connected users and locks.

Another way to get a list of your currently connected users is through a few quick lines of Python: ...