How we cite our quotes:
"Are you Saphira?" […]
Yes. Something clicked in his head and her voice echoed […] Saphira started humming. (7.31-32)
This is a significant moment in Eragon's relationship with his dragon. Saphira becomes more a "person" to him through this act of naming. As we'll see later, Saphira's name has a history behind it, too. In both cases, the identities of dragon and Rider are linked with the past and with each other.
It struck him then just how old the Riders were. A legacy of tradition and heroism that stretched back to antiquity had fallen upon him. (16.90)
Let's take that metaphor literally for a minute. How do you think that legacy would feel if it fell on you? Would it feel like a gentle, protective cloak, wrapping your shoulders securely? Or would it feel like someone had shoved an anvil in a backpack and strapped it to your body? Is Eragon's identity as a Rider a blessing, a curse, or perhaps a bit of both?
"To everyone else, I will be Neal and you will be my nephew Evan. […] I don't want our names in anyone's heads." (23.26)
You got it, Brom. Er… we mean Neal. Yeah, Neal, that's it. Here we see that Eragon's identity can be a thing of danger, as well as a source of pride. Being known as a Rider can win him acclaim, but it can also attract powerful enemies. That's why he and Brom have got to put on those fake Groucho Marx glasses before they go in to Teirm.