She feels like she should introduce herself, but that's a whole other can of worms. A Servant's true name is important and technically she already screwed up by giving her sword's name. If he'd been familiar with it, he could've identified her. She's at a real loss here, so for now, she'll just go with a simpler solution.

“Call me Saber.”

That works well enough for now. Not Saber of Red, that doesn't apply here, so there's no need to specify factions unless the other one shows up. And if he does, that's a whole other mess she's not going to think about unless she has to.

“And your dad made that?”

That's kind of awkward for her since she's wielding a sword she stole from her dad, but she'll try not to dwell on that anymore than she already is.

“All right, if we find it, I'll give you a chance to show it off too.”