How is this name properly spelled? It seems to me, an "Elliott" for over six decades, that the majority of us spell our name with all seven letters, no matter how redundant that may seem.
One justification for the second "T" is in the pronounciation of similar words:
IMHO, two t's are required to be sure that the "o" is short when the "o" is preceded by a vowel! Otherwise it looks French, how dreadful!, and is pronounced with a long "o" sound.
Another explaination is that residents of England have generally used the seven-letter spelling, and the Scottish have used the six-letter, one-T, spelling. Hence, the Elliott Cresson Medal and the musical "set in a northern mining town," "Billy Elliot". My heritage is (southern) England.
For more information on this, see my Database of spellings of Elliott