In Greek the subject of the verb is in agreement with the verb in the person and number.
O Γιώργος τρώει. = George is eating.
Ο Γιώργος is third singular person. The same person and number (third singular) is also the verb.
If there was an adjective defining the noun Γιώργος, of course it should be put in the same number, case and gender, as the noun.
O Γιώργος ο ψηλός τρώει. = George the tall is eating.
Γιώργος: masculine, nominative case , singular
ψηλός: masculine, nominative case, singular
Agreement is not required between the verb and the object. If there is any agreement, is absolutely accidental.
Η Μαρία βάφει τους τοίχους. = Mary is painting the walls.
Η Μαρία: feminine, nominative, singular
Τους τοίχους: masculine, accusative, plural
If there was an adjective or pronoun defining the object, of course they should be in agreement.
H Mαρία βάφει αυτούς τους τοίχους. = Mary is painting these walls.
αυτούς is a pronoun defining the object τους τοίχους, so they are in agreement.
αυτούς: masculine, accusative, plural
τους τοιχους: masculine, accusative, plural.