We don't have in-language names for each of the letters/runes yet, so I went ahead and devised some.  

AA - aan
A - ah
AH - hah
B - bey
D - dah
E - en
EI - hei
EY - ney
F - fo
G - gah
H - hes
I - in
II - kii
J - jen
K - ko
L - li
M - mah
N - ni
O - ot
OO - soo
P - pah
Q - qo
R - rah
IR- hir
UR - nur
S - set
T - tag
U - un
UU - huul
V - vei
W - wo
X - nex
Y - ye
Z - zo
 

I wasn't overly concerned with avoiding homonyms since many of the English letter names are also homonyms/homophones.  Any thoughts or suggestions?

While it may seem overly general and trite to say so, I think this is wonderful the way it is. Each is quite unique to its letter and sound. 

Nox!  My main focus was to keep it simple and make sense.

The only thing I'm not sure about are the vowel-letter dipthongs that have letter-names that begin with something other than that sound.

I'm trying to think of examples....

But no language I know has letter-names that begin with anything other than the letter-sound, except for loan-letters in Spanish like W and Y. Alpha Epsilon Eta Iota Omicron Upsilon Omega. Ay/Ah Ee/Eh Igh/Ee Oh Yu/Oo. Maybe use Greek as an example of how to differentiate "same-vowel-different-sound" letter names?

A ah

AA ata (or something like that)

AH aar (ditto)

E eh

EI eit

yadda yadda.

However, I also don't see a need to "keep it logical" based on our own world's languages, because it's not our world. I was just thinking about this a minute ago, how our own world's languages influence Dov language construction too much.

So... if no one else has my same concern, I say, cool. Let's go with that. (As images of baby dragons learning the alphabet pop into my head.)

The canon language is essentially English with a different lexicon, so if anything we've only made the language less like English.  In-universe, the Dragon Language and Atmoran Ehlnofex language would have directly informed the Nordic language, which in turn was the predecessor to Cyrodiilic along with the language spoken by the Nedes.  In other words, our languages aren't influencing the construction of the Dragon Language.  It's the Dragon Language that influenced the development of our languages (in-universe, anyway).

Another alternative for the alphabet would be to name the letters after actual words, like the phonetic alphabet.

about the phonetic alphabet:
I asked a friend (he has a linguistic qualification) of mine if he could make me a phonetic alphabet of the dragon language and send him sound examples.
I don't know when he will do that or if he's able to do it with the examples I sent him… but I'll tell you about it when I know more!

Awesome, that would be great!