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 a 2008 version of Mando'a, along with a script that includes custom letters for diphthongs and digraphs. 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 inspired by that original guide (the version below eliminates the dipthong and digraph combination letter, and uses "chah" for "c"). 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