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Oliver: Now, why do I get the feeling you're not my
10 o'clock from the Steel union? His appointment from the steel producers?

Zatanna: Zatanna.We weren't properly introduced.
Oliver: "Zatanna." Lose a bet with that name? Meaning she could be
fortuneteller with a name like that?

Zatanna: It's a family thing. Her name is a heritage?
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MadhulkOliver: Now, why do I get the feeling you're not my

10 o'clock from the Steel union? His appointment from the steel producers? Yes - his ten o'clock appointment.

Zatanna: Zatanna.We weren't properly introduced.

Oliver: "Zatanna." Lose a bet with that name? Meaning she could be

fortuneteller with a name like that? I would guess it was a race horse. (It's a question. "Did you lose a bet . . ?") I'm not really sure.
Maybe, "If I'm wrong, you can call me "Zatanna!"


Zatanna: It's a family thing. Her name is a heritage? Yes - a "given name" common in her family.
Thanks for your help, Avangi!
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MadhulkOliver: "Zatanna." Lose a bet with that name? Meaning she could be
fortuneteller with a name like that?
I take this to mean that Oliver is saying "did you get saddled with that name as a result of losing a bet."
Oh, a nickname. Thanks, Ray!
MadhulkOh, a nickname. Thanks, Ray!

Not a nickname. I take it from the dialog you quote that Oliver is something of a jerk. He is being deliberately rude in asking the question about Zatanna's name. He saying that it is sufficiently odd that the only way Zatanna would use it is if she were obligated to do so as a result of losing a bet.
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That's what I meant. A nickname as a result of losing that bet.