Do NOT operate the vessel until you have the documentation changed! Your documentation becomes invalid as soon as you alter the marking (Name and Hailing Port). Fines are steep, I think about $10,000 a day although the probability of their actually being assessed is low. Still, you could face a mountain of paperwork if the UCSG boarded you.
If the government does shut down, I suggest you put the old name back on before untying the docklines.