I'm puzzled by the premise of this being the only ship to survive the Burn. I think they said in DSC that only the ships whose warp reactors were active at the time were destroyed. In a huge Federation, there would surely have been hundreds or thousands of inactive ships at that moment.
Also, the last surviving ship being named Omega is a huge coincidence, unless it was renamed to that after the fact.
Also, the last surviving ship being named Omega is a huge coincidence, unless it was renamed to that after the fact.