
After the challenge by D. C. B. Marsh of the American Cryptogram Association on October 22nd 1969, invoking the name of Edgar Allan Poe in his address to Zodiac to reveal his name, he must have hoped that the Zodiac Killer would employ methodology featured by Poe, such as the ones described in his famous essay entitled "A Few Words on Secret Writing". The first three cryptographic methods detailed in Poe's essay were the scytale cipher, which can be used to decode the 340 cipher. The second cryptographic method told of splitting the alphabet in 13 characters of A through M, and N through Z. The Zodiac Killer supplied us with a 13-Symbol cipher on April 20th 1970, beginning with A and ending in M. The third cryptographic method (based on the second method) described two circular pieces of pasteboard, one on top of the other, each containing 26 letters of the alphabet in 26 segments, radiating from the center. One disk was fixed and one was moveable. See here.

The Zodiac Killer may have employed a variation of this technique by using a right shift of 8 in his 13-Symbol cipher, encircling the number 8 to denote the use of a Caeser Cipher Wheel. By placing a wheel or circle around the number 8 in the 13-Symbol cipher, the Zodiac Killer may have been telling us to rotate through 8 positions of the cipher to reveal his name. Of course, the Zodiac Killer was never going to give us his name, but he could have been playing one big joke.

After nearly four years of this code being unsolved, the Zodiac Killer may have thought it time to give us the answer by mailing us the Exorcist letter on January 29th 1974, offering us the words "Signed, yours truley" followed by a verse from The Mikado's Tit-Willow. When you examine the complete verse of Tit-Willow, you will notice eight consecutive letters of the alphabet spelling "My name is".
The only other place this is found is in the introduction to the 13-Symbol cipher on April 20th 1970. In other words, we can only connect the phrase "My name is" to these two communications.
The phrase "My name is Me" is a statement of identity, often used playfully or to emphasize a unique connection to oneself. In the July 31st 1969 letter to the San Francisco Chronicle the Zodiac Killer wrote "In this cipher is my idenity". On August 4th 1969 he wrote "By the way, are the police having a good time with the code? If not, tell them to cheer up; when they do crack it, they will have me".