There's not a way to do it directly into the native project name field, but you could get clever with a concatenated calculated field in a project custom form. I did this at a previous org where the creative team had a specific naming convention for their projects but they didn't want to rely on the project managers to always remember to enter it in correctly (or at all). They had a project form already on all of their projects, so I added a couple fields they wanted into the project name and added a calculated field to concat them, it was something like BU-Entry Year-Channel-Short Project Name (the native project name like XYZ Campaign Emails). The concat field would be what was used in all of their reports as the project name, instead of the native project name.
If you have Fusion you could maybe entertain a scenario to name the projects a certain way when they're created but not sure if it can do that.
If this helped you, please mark correct to help others : )