الرَّجُلُ is definite because of al-, not because it is a proper name.
جَاءَ الرَّجُلُ — The man came.
رَأَيْتُ الرَّجُلَ — I saw the man.
مَرَرْتُ بِالرَّجُلِ — I passed by the man.
There is no tanwīn because of the definite article. The normal genitive kasra remains; the absence of tanwīn alone does not establish diptote status.
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Definiteness and Proper-Name Status in Diptote Rules
الرَّجُلُ is definite because of al-, not because it is a proper name.
جَاءَ الرَّجُلُ — The man came.
رَأَيْتُ الرَّجُلَ — I saw the man.
مَرَرْتُ بِالرَّجُلِ — I passed by the man.
There is no tanwīn because of the definite article. The normal genitive kasra remains; the absence of tanwīn alone does not establish diptote status.