Here is the revised and polished translation, closely adhering to your instructions and the origin_text:
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"What's wrong with the surname Jarvis? Sylvia chose it herself," Old Mr. Jarvis argued, standing his ground.
"That's only because she hadn't come back to the Quintin family before. Now that she has, her name needs to be changed," Old Mr. Quintin replied stubbornly, refusing to budge an inch.
Old Mr. Jarvis asked, "Nana is just her nickname. What was her full name before?"
At that, Old Mr. Quintin's expression grew somber. "From the moment Nana was born, Georgia and I started arguing. Not long after, she left J City with Nana and gave her the nickname Nana. Later, when they came home, I kept saying we needed to give Nana a proper name, but every time Georgia and I disagreed, so we never settled on one."
Old Mr. Jarvis brightened. "Well, that just means Sylvia was the name she was meant to have all along. I don't think it needs to be changed!"
Old Mr. Quintin snorted. "Absolutely not. Tomorrow, I'll discuss this with Georgia, and then we'll have Nana officially registered under our family."
"You should ask Sylvia how she feels about it," Mr. Carnes interjected. "You can't just decide for her—what if she gets upset?"
Hearing this, Old Mr. Quintin hesitated a little, then finally said, "Of course, Nana's agreement is what matters most."
He glanced upstairs, a touch of emotion in his voice. "Tonight, Georgia and Nana are sharing a room."
Old Mr. Jarvis smiled. "Mother and daughter have known each other for a while now. This should help them feel less awkward and distant."
"Yes," Old Mr. Quintin sighed. "The more I look at Sylvia, the more she seems like one of the Quintin family."
Old Mr. Jarvis teased, "Weren't you the one who looked down on her before?"
Old Mr. Quintin flushed with embarrassment. "At that time—"
"What about it? You let Evelyn stir things up, and you developed a bias against a girl you'd never even met," Old Mr. Jarvis retorted. "You can't blame Sylvia if she doesn't pay you any mind."
Old Mr. Quintin's face reddened further. "That was my mistake!"
"Admitting it is good enough."
Old Mr. Quintin frowned. "But even now, Nana still hasn't called me Grandpa."

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Comments
The readers' comments on the novel: Find me in your labyrinth (Stella and Jonathan)
May we have updates please....
I wanted to see Gab courting Sylvia..probably that is yet to come. Please keep updating...thank you...
Maybe Gabriel can have someone at the Citadel check the whereabouts of Evelyn's boyfriend, whom she followed there in the 1st place to get information about her adoptive family and her biological family as well. The sooner she's gone the better. Thanks for the updates....
.........still hoping to see updates...
Awaiting more updates.......
Helllooooooo...
Yes, can't wait to see how gab is going to win over Sylvia. Please share updates...
Waiting patiently for the updates, thank you....
Thank you for the updates, this is so exciting now that Sylvia is connecting with her family....
Yea, so glad Mrs. Winters and Evelyn got caught. Thanks for the updates....