I know that Obi-Wan knew that Count Dooku was Qui-Gon Jinn's master. But did Obi-Wan mention to Anakin that Qui-Gon Jinn's master was Count Dooku? Surely,it would be more interesting for Anakin to have knowledge of Count Dooku's life as a Jedi.
We know that Dooku was a well-known figure among Jedi, one of the (in)famous "Lost Twenty" Jedi who'd left the Order.
He is numbered among the Lost: the Jedi who renounced their fealty to the Order and resigned their commissions of Jedi Knighthood in service of ideals higher than even the Order itself professed. The Lost Twenty, as they have been known since Dooku joined their number, are remembered with both honor and regret among the Jedi; their images, sculpted from bronzium, stand enshrined in the Temple archives.
In the novelisation for the Revenge of the Sith, it becomes apparent that Obi-Wan and Anakin are well-prepared for an encounter with Dooku, anticipating his fighting style and luring him into a trap by feigning different fighting styles that mimic their masters.
Kenobi’s Master had been Qui-Gon Jinn, Dooku’s own Padawan; Dooku had fenced Qui-Gon thousands of times, and he knew every weakness of the Ataro form, with its ridiculous acrobatics. Star Wars Episode III: Revenge of the Sith - official novelisation
Given the stress the Jedi put on the evolution of fighting styles when assessing each other's strength and weakness (from master to apprentice and back again) it seems unthinkable that when they were formulating a plan to fight Dooku, they wouldn't have given considerable thought to who he learned from, who he taught and how that would ultimately influence his swordsmanship.