a. They called their kitten Shadow. Objective Complement (This renames the direct object, kitten, as Shadow).
b. The jury deliberated four hours. Adverbial Objective (It answers the adverb question how long?)
c. Julia was awarded the starring role. Retained Object. (Your clue here is "was awarded" - this is in passive form. Passive form indicates a retained object.)
d. They appointed Geoffrey president. Objective Complement (This renames the direct object, Geoffrey, as president).
e. Nicholas was offered a magazine. Retained Object. (Your clue here is "was offered" - this is in passive form. Passive form indicates a retained object.)
f. We hiked three hours. Adverbial Objective (It answers the adverb question how long?)