I just recently realized that "Dr. Noonian Soong" and "Khan Noonien Singh" sound familiar. Is there documented confirmation that the TNG writers were inspired by Star Trek II? Or is this purely a coincidence?
Directly - no.
They were both named after Kim Noonien Singh, who Gene Roddenberry knew during World War II.
Additional trivia from IMDB:
During World War II, he had a friend named Kim Noonien Singh; after the war Kim disappeared, and Gene used his name for some characters in the Star Trek series (Khan Noonien Singh from Star Trek II: The Wrath of Khan (1982) and Noonien Soong from "Star Trek: The Next Generation" (1987)) in hopes that Kim might recognize his name and contact him.
Roddenberry also had a tendency to reuse names - for example, Dylan Hunt was used several times.
I just finished watching Star Trek Enterprise S04E04-06 and it's about Dr. Arik Soong. He was in prison for crossing the line when he was on the project creating the genetic supermen, the same as Kahn. The episodes also have Dr. Arik Soong's children, not his literal children but a group of kids he raised that were genetic supermen. He stole the embryos when he was working on the project.
At the very end of ep6 Dr. Arik Soong expresses his interest in making an android....... Inception of Data ;-)
Interestingly, one of the supermen children made mention of rumors of the ship "Botany Bay" (the ship that carried Khan and his crew) and Khan but Dr. Arik Soong dismissed it as not being true.
So they are not directly linked but thought it would be interesting to mention this.
Dr. Noonian Soong is in fact linked to Khan. Dr. Soong's great grandfather Arik Soong created the Augments (a second attempt at the kind of super beings led by Kahn) and played a vital role in the Eugenics Wars. Khan's name is a bastardisation of Soong's name, but Kahn is (in a weird kind of way) Noonian Soong's great great uncle.
And I quote:
'They retrieve the Augments' creator, Doctor Arik Soong (Brent Spiner)' (Wikipedia, under the augments)
Arik Soong was a criminal and the great grandfather of Noonien Soong. (ie creator of Data, Lore, B4)
I can understand why there is confusion, both the Soong men have an outrageous trait in the shows, they seem to live forever. Noonien Soong was at least 100 years old when Data finally met him in 2367, and Data himself was at least 120. Arik Soong himself is no exception, the Eugenics Wars take place until 1993 on Earth, yet Arik appears on Enterprise in 2155 roughly 150 years later (and looking mid 40s to boot).
It is further frustrating that Arik (Near the end of the episode) confesses his desire to create artificial life forms, a hobby which defines the existence of his great grandson Noonien Soong. Combined with his (Arik's) uncanny similarity to both Data (the positronic androids) and Noonien Soong (all played by Brent Spiner), I can understand why everyone is so confused.
The Augments and Kahn were created during the 20th century before the Eugenics War (1960s and 70s I'd guess) (look up the book Eugenics Wars, it details where and how the Bontany Bay and Kahn were created, and the Super humans rise to global power on Earth until 1996) I am unsure if Arik is directly mentioned, I doubt it, as Arik Soong is an ENT concept created for the Enterprise show, thus a decade or two (in real life) after Eugenics War was written.