Can someone name this part of the roof please?
I'm not sure there's an official standard name for this specific scenario, but I'd call it a purlin or an elevated wall plate, maybe. A diagram in this discussion has it as a raised top plate. This article discusses purlins as an intermediate rafter support member.
jwh20 is right in that this is a non-standard roof framing method, but there are a few reasons it may have been done (one of which you mentioned--attic space). Another is to create an &quot;energy heel&quot; or &quot;raised heel&quot;, where there's more vertical space for insulation. Yet another would be to raise the fascia/soffit height to clear windows or improve appearance (in the case of a very steep pitch). In your case the ceiling joists may have been run through to create backing for the soffit, which is often added later at a lower level.