I am looking for a method to allow the project notebook in a SharePoint site to be automatically named when a new site is created. I want the site title to be reflected in the project notebook. Is there a way to set this up inside of a site template?
I haven't looked at this for a while but I guess the Notebook has the name of the site that was used to create the site template? If so, a way around it is to move away from custom site templates, use the default "Project Site" template on the EPTs then have a process that deploys your custom artefacts to the project site after creation. Using SharePoint PnP remote provisioning is ideal for this. This is what we always do now. It makes it very easy to roll out changes to existing project sites etc. Details on the PnP remote provisioning here:
Otherwise, you could look to build a scheduled script that programmatically renames the file in the Site Assets library to match the Project Name. The code could run in an Azure function or Azure WebJob etc.
If you are using custom site templates, without custom code, the only option is to rename it manually via the Site Assets library.