[No elaboration on the point though- given how he reacted to hearing of his own death to save Shirou the last time, she knew better than to bring up details of her timeline.]
...I have no real preferences as to how you refer to me, but which name would you rather I use for you? When others are not around, of course.
[Even if he did want her to call him by his true name, she obviously wasn't going to do so in the presence of people who didn't know it!]
no subject
My true name... is Emiya.
[He doesn't specify it as Shirou Emiya. That's a name he's abandoned a long time ago. It was just Emiya now.]
no subject
[No elaboration on the point though- given how he reacted to hearing of his own death to save Shirou the last time, she knew better than to bring up details of her timeline.]
...I have no real preferences as to how you refer to me, but which name would you rather I use for you? When others are not around, of course.
[Even if he did want her to call him by his true name, she obviously wasn't going to do so in the presence of people who didn't know it!]