first all arts and styles are mixed. karate is a mix, hapkido is a mix, wing chun is a mix.
i call what i do Jissen Kempo Jujutsu. not because im some kind of soke, grand pubah 12th dan...but because all my influences can be listed accurately under that heading.
kempo=can (and has been) used to describe arts that are already labeled kempo (kenpo, kajukenbo) as well as arts formerly having been called kempo (many karate systems and tkd) ..and also as a show of respect to the chinese influence to all these arts. (chuan fa/kempo)..even more simply it can refer to the striking aspect of the arts. and certain characteristics shared by most if not all kempo systems.
jujutsu= again literal jujutsu, and a general term to refer to the grappling/locking/throwing aspect, as well as the strategy of "giving way"
it also shows my opinion that you should strike before you grapple. set it up, or it probably won't work. so it also shows the overall strategy i generally follow: start on the outside and work your way in (and down) as needed. set up your throws and locks with strikes.
my base: kempo jujutsu ...a system called gokei ryu. didn't study it long, but it made a big impact on my and how i look at things. it was sort of traditional, yet sort of modern as well. from there i studied taekwondo for about a year or so, still use some of the kicks, but didn't like the sport/mcdojang aspect, so i went back to kempo jujutsu for a while. after a while i stopped training full time formally, and just practiced and learned from anyone i could whether it ws in person, books, videos, conversation...etc.
all in all, i try to see the value in everything. as Dan Inosanto said "everyone has something to offer" and to me..knowledge is knowledge. some people prefer to stick with one art and learn all they can about it, others cross train. knowledge is knowledge, so to me both approaches are equally valid.
most of the time i just say i do kempo as we use it as short hand for kempo jujutsu. and much like karate or kung fu is used today..kempo is a general term for martial arts.