Yes, the 406 rim will work with a Durano 406 tire.

There are two versions of 20" tire, the 406 and the 451. Both sizes designate the diameter in mm at the bead. The two sizes are not interchangeable; so you have to make sure you get the correct 20" rim and tire. AFAIK, Schwalbe follows the ISO standard of tire designations. 406 tires have a decimal size, i.e. 20x1.125, while 451 tires have fractional designations, i.e. 20x1 1/8. Continental does NOT follow this standard. Caveat emptor.

BTW, the 406 size is the same bead diameter that most common BMX bikes use and come in widths from .9" to over 2".