You can assign by default one or more members when creating a task, including the task creator.
Project > "Settings" icon at the top right of the project window (below the user drop-down menu). You access the project settings. Go to "Collaboration on project" section.
Check the "Assign task creator by default" box and / or the "Assigned by default" box facing the desired member(s).
Leave all boxes unchecked if you don't want any member (or yourself) to be automatically assigned when creating a new task.
Each time a new task is created in the project, your settings will be applied.
Note: You can also add members directly to the project by typing the member's name in the "Search or create a member" field. If the member does not exist in your list of members, it will be automatically created and added to the list of project members.