The accepted order of the Mando'a letters is the same as English, because the script was created as a cipher for English and well before the language was created. (When I sort my Mando'a dictionaries, I don't try to get fancy and I just use whatever rules are included with my word-processing program.)
No canonical or common fanon names exist for each of the letters. Mando'a Lessons has a video about how to pronounce them, which you could use for inspiration if you'd like: https://www.youtube.com/watch?v=-wRs65XyvHI
A fan group adopted letter names from an older fan version of Mando'a, along with a script that includes custom letters for diphthongs. I haven't seen too many people use these names, but I don't haunt every place Mando'a is used on the Internet. You can find the most recent version of this specialized alphabet here: http://mandoa.ru/grammar_rules/eng
A quick reference from that original guide. This list presents only the names for 25 of the 26 letters that appear in the Mando'a script; there is no name for "q," which is not used in Mando'a words anyway.
a — ah
b — be
c — chah
d — da
e — en
f — fhar
g — ghar
h — hah
i — in
j — jah
k — kah
l — leh
m — mo
n — ne
o — ohn
p — peh
r — ra
s — sah
t — tah
u — uhn
v — voh
w — wen
x — sheh
y — ye
z — zhar