Quick answer: present DC DMV with an assignment of title, an original death certificate, and either letters testamentary/administration or an authenticated copy of the small estate order that includes the vehicle.
The small estate order itself is accepted proof
Only one TOD beneficiary is allowed
Designating a beneficiary for a vehicle title allows that person to obtain the title upon death without going through probate — but only one beneficiary can be added to a DC title, not multiple.
A trust can't receive this designation
A trust is considered a business for this purpose, and a beneficiary can only be added to a vehicle owned by an individual — a genuinely specific restriction worth knowing before relying on this option for a vehicle titled to a trust.
A will can't override an existing designation
A will or probate court decision does not override a beneficiary on a DC title, since the owner must be alive when adding the beneficiary — once made, the designation stands regardless of what a later will says.
A local probate attorney can review your estate — many offer a free consultation.
DC DMV processes these transfers the same way for every applicant, since the District has no separate county-level DMV offices.