A few years ago while in DC, we noticed a Transportation Museum just off the Mall. Does anyone know the 'official' name so that I can google it? Thanks for any/all information.

Could you possible mean the Smithsonian's Air and Space Museum?

probably the transportation hall in the Smithsonian American History museum - which just closed for renovations

The National Postal Museum across the street from Union Station (the train station) has many transportation exhibits and is very interesting. It is not really about stamps (although they are there). It is about how the mail was delivered.

American History on The Mall is closed for 2 years at least for renovations. There were transportation exhibits there as well.

Those are the only two museums that have transportation exhibits.