No, the Interstate system is owned by the states, DC, and Puerto Rico (There are three unsigned interstates in PR). Federal money is granted to the states to build a portion of it (Chargeable interstates), other portions are built out of state funds only (non-chargeable interstates).
The US government owns one bridge in Washington, DC only.
Aside from a few notable exceptions (Interstate 99, the Bud Shuster vanity road) the designation of roads in the system is controlled by the American Association of State Highway and Transportation Officials (AASHTO).
Yes, I’m a Road Geek.
If I remember my history (but sure it has changed) President Eisenhower initiated the Interstate system based on what he saw in Germany after WWII ... so now I guess it’s the states that control it and can do what they want which I think is not what he had intended ....
There's apparently another oddball-numbered interstate being considered: Interstate 3 (named after 3rd Infantry Division, IIRC). It will run from Savannah, GA to near Knoxville, TN. There is already opposition growing (because if it's built, we're doooooooooooooooooooomed).
By coincidence, George Strait owns one bridge...the Golden Gate (at least he implies he does in his "ocean-front property in Arizona" song). But that's part of US 101, not the interstate system.