From all appearances, it seems Titan in the MCU is indeed a planet in it's own right and not the Saturnian moon of the same name.
For one thing, we clearly see humans walking around unprotected on the surface, something that's certainly not possible on the real Titan since 1) There's no oxygen. And 2) it's cold enough for methane to condense into a liquid.
And it's not just the atmosphere; the whole environment is wrong. Temperature, gravity, local planetary bodies (Saturn itself is certainly nowhere to be seen!), relative brightness of the sun. None even remotely similar to the "real" Titan.
Finally: if Thanos' homeworld is mere light-minutes away, why did he need Loki to open a portal for his Chitauri? Granted, Sanctuary may or may not have been near Titan, but you'd think it'd be close enough that the extra leg to Earth would hardly be any trouble at all.
As for why there can be two places with the same name; leaving aside the fact this happens all the time in the real world (just look at an atlas!) The moons of Saturn were only discovered and named by astronomers in the last few centuries and they drew the name from Greek mythology.
There's a clear precedent in the MCU for at least some human mythological figures and stories to be of extraterrestrial origin, so it's certainly possible that the Titans of Greek myth are based on stories of Thanos's people, perhaps passed down from visiting Asgardians or Kree in pre-history.
In which case, Saturnian moon would unknowingly be named after the planet seen in IW.