Is this the only one or are there others defined by other sign conventions?
As has already been mentioned - there are essentially two but the Koszul one is amongst other things, the only one which makes the tensor product of complexes a complex.
Since I have been interested in this topic of late, I would point you towards the following internal (within MathOverflow) references:
For a recent discussion see: Tensor product of linear mappings versus chain complexes
In particular Simon Letner and Qiaochu Yauns' answers provide a nice conceptual backdrop.
I also found Theo Johnson-Freyd's answer here quite illuminating: References for sign conventions in homological algebra
Theo Johnson-Freyd's answer in this thread is also instructive: Sign convention for derivations in CDGAs
