Adverbial and Complement

In these two sentences:
1. I named the cat Pitty.
2. I call her Mum.
Could you tell me what kind of element sentence "Pitty" and "Mum" are, object, adverbial or complement? why?
Someone said to me that "Pitty" was complement, "Mum" was object. Is this right or wrong?
Thanks,

What did you call it?

'what' is not a question word with which we elicit adverbials.

Petty and Mum completes somehow the two direct objects, cat and her respectively. Thus, they are object complements.