I have found an arrival record (Ancestry.com) for Annelise Morgenthau, age 20, arriving in New York on 26 Nov 1947 on the ship Marine Jumper. Her visa number is given as QIV 6631 (issued on 26 Sep 1947 in London), and an annotation on the second sheet implies that she is intending to become a permanent resident. She is coming to join a friend or relative who is listed as F. Kahn:

Kahn is Annelise's mother's maiden name, which gives me more confidence that this is the right person. Perhaps she is coming to join her uncle...
Unfortunately, I cannot find any other trace of her in the US, and would like to explore the possibility that I can find her naturalization papers through the visa number and date of issue.
What is the right way to proceed? How do I find a naturalization request or other pertinent information based on the entry visa number?