Get the "name" property from a BPA enumeration

Only the id of the selected user task enumeration is readily available in the execution. Your easiest option is to introduce a duplicate json to execution that holds the enum in user form.

 Script task 1:

var json = '{"enum1":[{"id": "DB_TEST1", "name": "Test1"}, {"id": "DB_TEST2", "name": "Test2"}]}';
execution.setVariable('json', JSON.parse(json));

Script task 2:

var jsonObj = execution.getVariable("json");
var sl = String(selectById(jsonObj, execution.getVariable('enum1')));
execution.setVariable('selected', sl);

function selectById(json, id) {
    for (var i = 0; i < json.enum1.length; i++) {
        if (json.enum1[i].id == id) {
            return String(json.enum1[i].name);
        }
    }
}

Be sure to place script task 1 after the last user task.

Another option is to add the enum name resolution by id logic as a projection function and call it via an API task where necessary.