From the books I have read, there is no definite source for how Dallas got its name. Quoting from Page 353 of "The Roadside History of Texas":
"John Neely Bryan, farmer, lawyer, and Indian trader, was the first settler, arriving in 1841 and building a cabin in what is now the western end of the downtown area, today's county government region...The Mabel Gilbert and James J. Beeman families joined him a year later, and the fledgling village became Dallas, probably named for George Mifflin Dallas, vice president of the US from 1845-1849. However, it could have also been named for his brother, Commodore A.J. Dallas of the US Navy; or their father Alexander James Dallas, secretary of the treasury; Joseph Dallas, a settler near the new town; or any of the brothers James R., Walter R., or Alexander James Dallas, all of whom served with the Army of the Republic."