The USDOT number will have to be new for the new owner. USDOT does not transfer. It is attached to the original name forever, whether in or out of business.
The MC is transferable. Requires a particular set of steps FMCSA MCS150 etc. There is a list of steps available online. A new MC# is $300.00. It is less expensive to process your own number. Unless, the buyer is looking for a strong safety or insurance history because theirs is weak and are hoping to become chameleon carriers.