05AB1E,  24 23  21 bytes

Assumes there is a noun for each name, as allowed by the challenge.

„'s«I¯ªâI‘ʒl€нË}Ωðý

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05AB1E,  24 23  21 bytes

Assumes there is a noun for each name, as allowed by the challenge.

„'s«I¯ªâI‘ʒl€нË}Ωðý

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Explanation

„'s«                    # append "'s" to all names in the name-list
    I¯ª                 # append an empty list to the adjective-list
       â                # cartesian product between the lists
        Iâ              # cartesian product with the noun-list
          €˜            # deep flatten each sublist
            ʒ    }      # filter, keep only lists that when
             l          # converted to lowercase
              €н        # with only heads kept
                Ë       # have all elements equal
                  Ω     # pick a valid list uniformly at random
                   ðý   # and join by spaces

05AB1E,  24  23 bytes

Takes input in the order adjective, name, noun.
Assumes there is a noun for each name, as allowed by the challenge.

)ªâsâε˜ć„'s«š}ʒl€нË}Ωðý

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05AB1E,  24 23  21 bytes

Assumes there is a noun for each name, as allowed by the challenge.

„'s«I¯ªâI‘ʒl€нË}Ωðý

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05AB1E, 24 bytes

Assumes there is a noun for each name, as allowed by the challenge.

„'s«IõªâIâε˜õK}ʒl€нË}Ωðý

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05AB1E,  24  23 bytes

Takes input in the order adjective, name, noun.
Assumes there is a noun for each name, as allowed by the challenge.

)ªâsâε˜ć„'s«š}ʒl€нË}Ωðý

Try it online!