As you probably know, there are as many names as there are different type of implementation of a project office. May be, this reflect the fact that project office is a fairly new concept that has not "cristalized" yet in the industry. The concept should quickly gain in maturity and should become a recognized organizational entity (just like any other well recognized function in a company). But no matter the name, the project office function is often to be a provider of project management services. My suggestion is to define your "mission" and the the project management services you want to offer in the company. The role of your project office should be clarified and of course should match your company needs. Then find an appropriate name so it "rings" a bell when people hears it. For example, if your project office is really to be supportive to project, to produce report, then perhaps Project Support Office is the appropriate name. If your project office is to provide methodology, advise then perhaps the name if Project Management Center of Excellence. Finally if the role is to be responsible to "deliver" projects then the name could "Project Delivery Office"
In all cases the role of the Project Office might evolve as your company project management maturity grows, then a name change might be required. Saving Changes...