In the 'Kamisama Hajimemashita' full story, the key characters are Nanami, a girl who becomes a god, and Tomoe, a fox spirit. There are also other important characters like Mizuki, another spirit who has a certain connection with Nanami. But Nanami and Tomoe are the central ones as their relationship drives much of the story. Nanami's journey as a god and Tomoe's changing feelings towards her are important aspects of the plot.
There is also Narumi Fujishima. He gets involved in the strange happenings along with Alice. His character development throughout the story is quite interesting as he faces different challenges and grows from them. Another important character could be the people around them who contribute to the overall plot by providing support, information, or sometimes being part of the problems they need to solve.
I'm not sure exactly as I haven't read it fully. But usually in such light novels, there would be a protagonist who is likely to be deeply involved in the situation of the god - less Sunday.
In a crossover with 'Naruto', Naruto himself would be a great addition. His positive and determined attitude could contrast with Tomoe's more reserved nature. And his powerful ninja skills could come in handy when facing some of the demons in the Kamisama Kiss world. Sakura could also be there, and she might bond with Nanami over their strong wills.
I'm not sure who the main characters are as I haven't read the light novel. But it could be the person who becomes a 'kamisama' and perhaps some characters who are either friends or foes in their new god - like life.
There are several mangas that share similarities with Kamisama Kiss. For example, 'Fruits Basket' has a touch of fantasy and romance like Kamisama Kiss.