عُمَرُ is a proper name. The book identifies it as an example of ʿadl combined with proper-name status.
جَاءَ عُمَرُ — ʿUmar came. عُمَرُ is the nominative subject, with ḍamma but no tanwīn.
رَأَيْتُ عُمَرَ — I saw ʿUmar. عُمَرَ is the accusative object, with fatḥa but no tanwīn.
مَرَرْتُ بِعُمَرَ — I passed by ʿUmar. عُمَرَ is genitive after bi-, but its case marker is fatḥa as a diptote.