After Rosemary was impregnatated by "Satan," many of the occult leaders that knew about this were obsessed with providing her "Tannis Root." What was the significance behind this "Tannis Root?"
In the film, Rosemary is sent a book by Hutch called All of Them Witches where she discovers the identity if her neighbours. One part of the book is underlined:
In their rituals, they often use the fungus called Devil's Pepper. This is a spongy matter derived from swampy regions having a strong pungent odor. Devil's Pepper is considered to have special powers. It has been used in rituals and worn on charms.
The talkative office receptionist (Marilyn Harvey) off-handedly mentions that Dr. Sapirstein also wears a smelly tannis-root cologne - marking him as a member of the witch's coven: "He has the same smell once in a while, whatever it is, and when he does, oh boy."
"The name is an anagram" doesn't refer to Tannis root. It refers to Roman Castavet. Recall when Rosemary uses Scrabble tiles to figure out Roman Castevet is really Steven Marcato.
Tannis root, with its mystic/magic property and bad smell, is simply a clever plot device used by author Ira Levin to demonstrate the power of the devil worshipers.
I've seen references to Tanis Root providing immortality, but I can find no hard documentation right now to support that theory. Tanis is also an Egyptian city. Shown in the movie Indiana Jones and the Raiders of the Lost Ark to be the resting place of the Ark of the Covenant. However it is normally spelled Tanis and not Tannis.
It IS an anagram, it's Tanas Root - when Roman mentions it to Hutch during Hutch's visit to the apartment, he's never heard of it and does some digging. Then, at Hutch's funeral, Grace, the woman who answered his phone while he was in a coma, gives Rosemary a paper-wrapped book and told Rosemary that Hutch said to tell her "the name is an anagram." Rosemary repeats the phrase "the name is an anagram" while she's reading the book and telling herself there can't possibly really be witches. So the movie itself states that the name - the name of tanas root, which Hutch had never heard of and did some research on - is an anagram. I don't know why I only see it spelled Tannis.