Air carrier Captain reported an NDB and VOR share DCA as an identifier even though they are not colocated creating confusion when entering the identifier into an FMS or GPS system.

Narrative

DCA VOR (111.0 MHz) and DCA NDB (332 kHZ) share the same three letter identifier despite the fact that the two navaids are physically located 5.6 NM apart. This causes pilot confusion when selecting the DCA navaid in an FMS or GPS navigation database. I believe this is a serious safety risk that the FAA needs to fix by re-designating the DCA NDB to another three letter identifier. Additionally; I believe the two navaids having the same identifier violates FAA Order 7350.9FF paragraph 1-2-5.It appears that the DCA NDB used to be the LOM for Runway 1 which was decommissioned in october but retained as an NDB. At that time the identifier changed from 'DC' to 'DCA.' There are only three examples total of shared VOR/NDB idents in the NAS and the other two involve facilities that are colocated on the airport (SYA and TUT). This is the only example of two navaids with the same three letter identifier that are physically not colocated in the same location or even on the same airport landing area. The FAA needs to resolve this ASAP.