Amane has a unique power: if she knows someone's true name, she can control his or her spirit. Because of her unusual stoic attitude and suboptimal social skills, she is seen as creepy by her peers and has a hard time making friends. The only "person" she really talks to is actually her guardian in disguise: Hyoue, a dog-demon, who feeds off of humans' life energy. Amane "feeds" him by kissing him in public, which doesn't with help her public image. Amane and Hyoue must keep their powers a secret while fighting the evil spirits they encounter.
If you liked Her Majesty's Dog then you will also most likely like Rasetsu or vice versa. All the while I have been reading this manga, I keep feeling like there are sooo many similarities between the two. Both have a strong female lead character that fights ghosts, and a link to the supernatural. Also, in Rasetsu there are many references to Kotodame, and in Her Majesty's dog, the girl only uses Kotodame. Both are very good manga. If you like one, then you will most likely like the other.
I don't exactly know what it is but after reading the first few chapters of 'Her Majesty's Dog' I instantly thought of Zodiac P.I.
They both have heroines that do 'secret work' which involves murderous activity. They also have some romance and have the same pace; every chapter is a new case. Her Majesty's Dog has more of a darker feeling whereas Zodiac P.I is very light and happy feel.
I personally like Zodiac P.I better since the drawings and the storyline is cutier but Her Majesty's Dog has a much deeper sense. But if you like one you are sure to like the other.