Allen's explanation of how he translates pyramid names:
"Pyramid names are composed of an epithet plus the king's name. The epithet refers to the pyramid (mr: masculine), not the king, as shown by the determinative and by the names of Khufu's and Amenemhat I's pyramids. The name as a whole is a direct-genitive construction. In abbreviations the second part of the construction, the king's name, can be left out."
The full name of the pyramid is for example: 'Khafra's 'Great Pyramid', / 'Khafra's Great Place', abbreviated to the 'Great Pyramid' / the 'Great Place'.
The pyramid is not an isolated structure - it was the most conspicuous part of the royal funerary complex, and the name of the pyramid gave the name to the whole complex. If a priest was on duty at 'Akhet Khufu', his actual duties were not inside the pyramid itself, but mainly in the royal cult complex that was usually on the east side of the pyramid - it was in the royal cult complex that the priests served the cult of the dead king.
The various parts of the cult complex were all named - we know from the Abusir papyri that the 'front porch' (rwt HAt) led to a vestibule with pillars called the 'House of the Great Ones'. This led to a 'court' / 'hall' (wsxt) with many pillars, two of which were called 'Great' (wrt). The royal cult complex appears to have been a model 'cosmos'.
The royal funerary complex also had funerary domains - agricultural estates that sent produce to the royal cult complex. The estates had their own names, 'Khufu appears' (xa.f xwfw); 'she who sees the power of Khufu' (mAt bAw xwfw) etc. Also a settled community served the royal cult with its own workshops etc. - in the case of Giza it probably served the whole necropolis - it took the name of the pyramid.
The reason I emphasize that strictly speaking the name refers to the pyramid itself, is that the pyramid was a manifestation of the king - we even have texts where a queen is royal mother of the pyramid of Pepi I; royal wife of the pyramid of [Meryre] etc.
In practice however, the name of the pyramid covered the whole funerary complex including the settled community that served the royal cult.
CT