Yes, you can use the History tool to save and label versions of your work in Overleaf.
These versions save the complete project (source code and attached files). With a free Personal account, you can retrieve previous versions of your projects from the last 24 hours, and once you label a version it will remain saved after 24 hours. With a paid subscription, you can always access all versions from your project history.
Access this feature via the 'History' link in the editor's top bar—simply select a version from All History and click Label version to save that version of your work indefinitely with a label.