Yes, it will! When you change the name of a project, the timesheets already submitted with the previous project name will automatically update with the new project name.
See the following screenshots to see how it works.
1. Open the Portal in your browser and select the "Projects" tab
2. Find the project you want to change and double click on it or select the edit icon next to it.
3. Click in the "Project ID" box to change the project name (ie: name changed from "Break" to "Break General")
4. Click on the save icon to save the change
5. Name has been changed and saved successfully.
6. To view the timesheets that were updated with the new project name, select the "Timesheets" tab in the main menu
7. Here you can see the submitted timesheets that have been updated with the new project name