The Oceanic logo is very similar to a Nazar amulet, used to ward off the evil eye, and a picture of one also features in the Room 23 Video.
There is always a mention of "lying" and hiding some truth that the Oceanic 6 are bound to.
The Oceanic Airlines logo looks like the island itself. The O is blue, like water and it surrounds the colors like an island.
Oceanic went out of business following the disappearance of Flight 815, it is possible that Widmore Industries (or one of its other interests) purchased oceanic or helped get the airline started again. Possibly to aid the cover up of the crash/island etc... or as some part of a bigger plot that we haven't seen yet.
If it was Widmore that staged the fake wreckage of 815, owning or being a part of oceanic would give him easy access to another identical plane to use as the fake 815.