There are no laws against being two persons - as long as the names aren't used for fraud or deceit. The old man will be transferring over to the new man only those things that are Godly. Where possible, liabilities will be terminated by the old man. Those things that cannot be terminated will be left for the dead to bury their own dead.31
All of the dead man's real and personal property must be sold or transferred. If the old man still has outstanding obligations, he has not yet died. It will become more difficult for the world system to continue making claims against the old man once the new man is actively bearing fruit unto the Lord and has no agreements with the world.
During the probate period, you will also be establishing your new name in your daily transactions. At this point you have two names. You will be closing out your state name and establishing the name given you by God. You will live the life of two people - for a transitional period only. It may take you thirty days to probate the old man's obligations. It may take a year, or ten years, depending on how diligently you take care of the things of Caesar.
The new name not only separates you from your old life of sin, but also helps keep you sanctified unto the Lord. For instance, let's say several years down the road you are tempted to apply for a state driver license. You arrive at the state motor vehicles division and find out they need two pieces of state issued identification. Since you have been reborn in Christ, you have no state documents. The state's own rules preclude the new man from succumbing to the temptation of obtaining a state license.
31 - Luke 9:60