Google Earth Engine: Name parameters in custom function

This happens to be a matter of pure JavaScript; when you write a function and call it yourself, the Earth Engine API is not involved at all.

Here is how to write your function to accept {} named arguments:

function get_sum(args) {
    var value_1 = args.value_1;
    var value_2 = args.value_2;
    var Sum = ee.Number(value_1).add(ee.Number(value2)); 
    print(Sum);
}

(args is just a regular function parameter variable, not a special keyword, and you can call it whatever you like. args is a common name for this sort of thing.)

If you want to accept either named or un-named (positional) arguments, like the EE API functions do, it's significantly more messy and I'd recommend not bothering, but if you like, I can explain that too.

Note that if you misspell a name, the variables in the function will have the value undefined. If you want to help yourself out at the cost of writing more code, you can check for that:

function get_sum(named_args) {
    var value_1 = named_args.value_1;
    var value_2 = named_args.value_2;
    if (value_1 === undefined) throw new Error('get_sum: value_1 is missing');
    if (value_2 === undefined) throw new Error('get_sum: value_2 is missing');

    var Sum = ee.Number(value_1).add(ee.Number(value2)); 
    print(Sum);
}

---

Side note: Current JavaScript versions support a shortcut that makes this much more convenient:

function get_sum({value_1, value_2}) {
    var Sum = ee.Number(value_1).add(ee.Number(value2)); 
    print(Sum);
}

Unfortunately, the Earth Engine Code Editor does not currently permit running scripts that use newer JavaScript features. I mention this only because you may see references to this feature when reading about JavaScript.