Some people refer to him as Rabbi Elijah Kramer. When I first saw this name a number of years ago, I didn’t know who was being referred to since I had never heard of any Elijah Kramer. The first reference in print to Elijah Kramer (or Kremer) that I have been able to discover is Maurice Samuel’s 1963 book, Little Did I Know, p. 257. (If anyone is aware of an earlier reference, please let me know) The name was later made popular after appearing in the title of Yaacov Dovid Shulman’s 1994 book, The Vilna Gaon: The Story of Rabbi Eliyahu Kramer.
If this post does nothing else, I hope it puts an end to this mistaken practice. The Vilna Gaon was not named Kramer! He was descended from someone named R. Moses Kramer (his great-great grandfather), but the Gaon never used this name and no one ever used it about him, so it is a mistake to call him this. See also note 1 in S.’s post here.
The mistake of referring to the Gaon as Kramer appears in a 2012 book by Rabbis Berel Wein and Warren Goldstein, The Legacy: Teachings for Life from the Great Lithuanian Rabbis, p. 130. The particular chapter I refer to was written by Wein, and on the same page that he mentions Kramer he refers to the Gaon’s foremost student as “Rabbi Chaim Rabinowitz”. As far as I know, this is the first time R. Chaim of Volozhin has been given the last name Rabinowitz, and I have no idea what led Wein to write this. Perhaps there was some confusion between R. Chaim of Volozhin and R. Chaim Rabinowitz of Telz.
Marc B. Shapiro, “The Vilna Gaon, part 3 (Review of Eliyahu Stern, The Genius)”, The Seforim Blog (23 February 2014) [http://seforim.blogspot.com/2014/02/the-vilna-gaon-part-3-review-of-eliyahu.html]