for doing that, please go to the page of that special publication and click on the 'more' button, which is placed just at the right side of the blue 'share' button.
In the drop down menue there is an 'edit' button, which allows you to get access to details of your publication.
In the 'author' section please press the 'Request edit' button. It will take some time until you get access to the author list. Once this list is available to you, you are able to edit/correct the author name(s).
Do not forget to 'save' your changes when leaving the edit page.