Japan doesn't seem to have an issue with using Spanish words for food (at least, not if パエリア is any indication). If we look on Wikipedia for arroz con pollo, we can see that their transcription is "アロス・コン・ポーヨ". That said, as with any language, you can use the native name if you want, but if the target culture has no concept of what it is, you're going to be describing it anyway. I would guess that if you just say "チキンライス" or something it won't really get the point across of what arroz con pollo is, so whatever you choose to describe it with will need to be detailed anyway.
There are other things to be careful about too, though. For example, I just tried looking up arroz con leche, and it seems that in English we call it "Rice pudding," and the corresponding Japanese concept is called ミルヒライス, which is actually borrowed from German!
The short of it is just look it up and see if the thing you're trying to describe already exists in the collective Japanese consciousness. If it doesn't, then translate it as an explanation of what the dish is and include the Spanish if you want to, similar to how you would translate "natto" into other languages.