Formula to select the name associated with lowest value from data set & a random name from the lowest options if tied

In Google Sheets, I have 4 Names associated with 4 data points that update throughout the month. I'd like to auto pick the name associated with the lowest data point. If there are 2, 3 or all 4 that have the same lowest point, I'd then like to select a random name but only from the lowest data points.

Ex Scenario 1 - The formula should select adam from the list.

Adam - 2Bill - 3Charlie - 4David - 4

Ex Scenario 2 - The formula should select a random name from the adam, charlie & david only.

Adam - 2Bill - 3Charlie - 2David - 2

Ex Scenario 3 - The formula should select a random name from the adam & bill only.

Adam - 1Bill - 1Charlie - 2David - 2

Any help in developing a formula would be greatly appreciated!