If I remember correctly, your first name never appears in Bioware sequels...
I could be wrong but I don't think that the Hero of Ferelden first name is shown in the Codex in DA2.
And the same in Mass Effect. Your commander is always refered as 'Shepard' and the first name appears only in the squad window...
This is true. I recall DA2's codex entries never giving the Hero of Ferelden's first name either.
so, how to explain you.....
i think, this could be a good thing, because we can personalize our own story and fill it with our own characters, and to create really our OWN dragon age's world etc, if you know what i mean. it's a little hard to explain....
but i hope you get it ! 
And sorry for my bad english ! 
If it helps: another reason not to worry, in addition to what Lucie_J24 said, is that one can customize Hawke's appearance in-game. No, Hawke's custom first name is never mentioned, but you can re-create his or her appearance (except maybe his or her hairstyle, if a match isn't in DAI). Plus, Hawke has the same voice actor/actress. Even better, unlike importing save game information from DAO/DAA/DAO's DLC to DA2, when importing the decisions into a new DAI game via the Keep, they are correctly reflected in-game! So, in-game, it's still your DA world that you helped create. Your custom Hawke's appearance and the choices your Warden and Hawke made, and which you imported into DAI, are preserved.
As for the Keep, while it is kind of annoying that playthrough states don't upload the custom name and image you had in the Keep, there's a way to change the default to custom. Go to World States in the left sidebar, then scroll right to Playthrough States. Select a playthrough state and select "copy to editable". Go to the Editable States and select the playthrough you just copied. Select the "load in Keep" button. Now, at the top of the Editable States section, it should say that the playthrough is loaded into the Keep, so select "edit in tapestry". Once back in the Tapestry, go to the hero section and select the custom Warden and Hawke as you normally would. Now that playthrough state has the custom Heroes' names and their images.
Frankly, I'd like it if we could upload our own images for the heories in the Keep. Take a screenshot of the Warden, Hawke, or Inquisitor, crop the image to just the head, and upload that.