I don't know the exact significance of the word "Darth" in the Sith world, but I think it was a word of honor for powerful Sith. That's why Anakin was given this title for his new name.
All powerful Sith in the canon had this word in their names: Darth Plagueis, Darth Bane, Darth Sidious, Darth Vader, Darth Maul, etc. As such name similarity can't be names given by their parents, I can assume they were given such title as an honour.
Now, look at Count Dooku... he was a powerful Sith too. So, why wasn't he given this title?
Darth word to address Dooku hasn't been used in the movies, as far as I know. If you are claiming that Darth and Lord words are the same, give citations because my vocabulary rejects it.