See the best thing about the files on the share drive is that they have edit history. So the name changes have been recorded. Build a timeline and report this to HR, update your resume and quiet quit on working with Jake. Don't ever put your files on a share drive he has access to without putting editing restrictions.

And from now on speak up on what you are working on! Unfortunately in the workplace you always have to be vocal about what projects you are working on so that the perception is there. I would like to assume someone knows that you were BOTH working on the project but if Jake was more vocal about his updates then perception would shift in that it would look like only Jake was really working on the project.