Assuming the decedent had properly registered the assumed names with the county and evidence of that registration is available to you, I don't see a problem with the estate continuing to use them temporarily. This is with the understanding that they are winding down these operations and have no thoughts of operating them for an extended period.
The relevant statute, KRS 365, provides for DBA registration for individuals and business entities. It does not indicate how or where an estate could register as a DBA.
In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.