Anakin was still very close to Obi-Wan, almost padawan close. Plus, being the one of the most well known, powerful and important Jedi directly involved in the War, he wouldn't have had any time to get to know the padawan. How would that padawan feel if there new master went running off to war for months at a time, leaving them behind, becasue that's just what Anakin would do. Feel bad about himself 'cause Obi's leaving him behind and being to cautious with his Anakin's safety, then Anakin get's his own Padawan and does the same.
Plus it wouldn't make sense canonically. When Anakin turned to the dark side, his padawan, seeing his master turn evil will likely follow the same path. Just doesn't make sense in the movie.
Not to mention he's the Chosen one, arrogant, and is secretly married. Obi-Wan's close enough to them, Anakin wouldn't want another person in on his private life.