Okay, in the books Lyra’s second name is Belacqua - a pretty cool name by all standards I’d say.
But why is it? Her mother’s second name is Coulter and her father is Lord Azriel, so where does Belacqua come from? 
I always thought that Asriel was his first name. Perhaps he’s Asriel Belacqua? Which, I have to say, is an improbably fancy name, but lords never seem to worry about that sort of thing.
Well I don’t know about in Lyra’s world but in this one if someone is a Lord the name following their title is their second name.
Remember, Lyra didn’t know at the beginning that Lord Asriel was her father. She thought he was her uncle, and her parents died when she was a baby. So, assuming those people were real (Lord Asriel’s sister and brother in law, maybe) , it’s possible that their last name was Belacqua, and that’s where her last name comes from.
Hmmm - as good an explanation as any I suppose.
I’ve read the series and this is how I understood it as well.
Now is it a coincidence that her name is Lyra and one of her main skills is lying? Of course, that adds irony that she is the only one who can utilize an alethiometer.