I tend to use the generated name (at least partially) for most systems I discover. However I will usually drop part of it, if it feels too clunky to me. Planets are mostly named after the star they orbit, and add one of the numbering/lettering systems below to it, then use that same naming scheme for the rest of the system.

I also know that as of this writing, there is a maximum of 6 visitable celestial bodies per system. I am going to provide more in my naming system in the hopes that eventually HG will put more stuff in each system.

Greek Alphabet
Latin Number Names Female
Latin Number Names Male
Latin Numbers
N.A.T.O. Phoenetic
Alpha
Prima
Primus
Unus
Alpha
Beta
Secunda
Secundus
Duo
Beta
Gamma
Tertia
Tertius
Tres
Charlie
Delta
Quarta
Quartus
Quattuor
Delta
Epsilon
Quinta
Quintus
Quinque
Echo
Zeta
Sexta
Sextus
Sex
Foxtrot
Eta
Septima
Septimus
Septem
Golf
Theta
Octavia
Octavus
Octo
Hotel
Iota
Nona
Nonus
Novem
India
Kappa
Decima
Decimus
Decem
Juliette
Lambda
Undecima
Undecimus
Undecim
Kilo
Mu
Duodecima
Duodecimus
Duocecim
Lima
Nu
Tredecima
Tredecimus
Tredecim
Mike
Xi
Quattuordecima
Quattuordecimus
Quattuordecim
November
Omicron
Quindecima
Quindecimus
Quindecim
Oscar
Pi
Sexdecima
Sexdecimus
Sexdecim
Papa
Rho
Septdecima
Septdecimus
Septdecim
Quebec
Sigma
Duodeviginti
Romeo
Tau
Unetviginti
Sierra
Upsilon
Viginti
Tango
Phi
Vigintiunus
Uniform
Chi
Vigintiduo
Victor
Psi
Vigintitres
Whiskey
Omega
Vigintiquator
Xray
Vigintiquinque
Yankee
Vigintisex
Zulu