Count Dooku has not been given any additional name in any material, canon or Legends
As far as we know, his first name might be:
What about "Jard"?
As far as I can tell, the name "Jard" was created by noted fan SuperShadow, who claimed to be a close friend of George Lucas and posted many previously-unreleased tidbits and interviews on his website1; Dooku's name was one such fact, posted on the FAQ section of his personal website.
Despite his claims, SuperShadow has no affiliation with George Lucas or Lucasfilm, and has never been a source of legitimate canonical facts; everything on his website seems to have been invented by him. Many of the claims posted on his website were later contradicted by canon sources, and Pablo Hidalgo has publicly denounced the site.
1 The website no longer exists, by the way; the supershadow.com domain is now owned by a Japanese company, and appears to point at a site advertising hair removal services