They should really just record several common first names into the voice acting, and limit the usage in dialogue to prevent an overburden on VO work.
Example: take 50 common male names, 50 common female, 25 gender neutral - and only use the first name in key scenes. So most characters will use Ryder, in the same way Shepard was used in the original trilogy, but there will be a few scenes (like in the romance scenes) where a character will have a short line using the first name. Maybe a love interest saying, "I'm here for you, [insert name]." It's not that hard for a few different VO actors to record "I'm here for you, [insert name]" 125 times with a couple of takes on each name. That's 250 takes of a line that takes two seconds - that's maybe a half day's work for the entire cast.
Also, I can see it being used early and late in the game when your character (which by all indications will be military) is recognized in a formal or military setting where they use the character's full name ("Lieutenant Commander Jane Ryder").
Even if it was only used a handful of times, I think the effect could be powerful in further cementing a player's feeling that they created a unique individual who shapes a galaxy.
Or they should just Pick a name for you.
Seriously I don't know about anyone else but I didn't pick the name I was given. Why do RPGs REQUIRE that the player pick the name? It doesn't actually make sense from the stand point of how people get names and if people are that insecure that they require to name the character before it is their character vs, Bioware's then I ask this... Are you not your own person even though your mother and father named you and you had no input at all?
Simply because it has always been done doesn't mean it should remain as such. There is zero reason from a development perspective and a reality perspective to require that the player picks the name of their character when 99.9999% of the entire population of the planet where given their names with no say what so ever. We only get to pick our names in video games because it is a tradition but now that technology is such that text is no longer the key form of communication is games it is time we change things so something far more realistic and a lot cheaper to implement than saying 125 extra line of dialogue for limited places in the game. Just give me one name.
This is something that other games are doing that are not RPGs there is zero reason for RPGs to blindly follow tradition. Just because something has always been done like X doesn't mean it is the best way to do things nor that we should blinding keep doing X.