My friends Majid and Sven are correct in analysing the name "MADHEEN-MADHIN"First I agree with them that it is Not Arabic.....Majid gave you few names that are close as MAHDI /
MADINA ect...It Is very common in Europe And the US that we write a word combined of letters from the sire or dame once these letters togother form a sound other than the romantic languages then it was considered different and maybe Arabic....My Take on the name MADHIN IS:
His Maternal grand father if I am correct is "MADHIN"Thru the foundation mare "MADINAH"
So the breeders took the liberty to reshufle the letteres to come up with
MADINAH===MADHIN (For a colt as the "A" has to be left out )
Your stallion was given the name of the maternal grandfather9which is very common in the desert) and adding the last two name of his sire Farid ...so you got" MADHIN NILE MOON"
as you mentionned start working on a good Arabic name to promote your gorgeous Stallion .Don't feel bad I have came across many famous stallions outside the Arabian world that their name has no meaning what so ever exept a bunch of letters put togother to create a sound that satisfy certain owners...
This practice is desapearing fast,thank God, as now we have means to research ,ask questions or aquire books that could help us in Naming properly our Arabian Horses..
Shoukran for listening