C# add validation on a setter method

If you want to validate when the property is set, you need to use non-auto properties (i.e., manually defined get and set methods).

But another way to validate is to have the validation logic separate from the domain object.

class Customer {
    public string FirstName { get; set; }
    public string LastName { get; set; }
    public string Organization { get; set; }
}

interface IValidator<T> {
    bool Validate(T t);
}

class CustomerValidator : IValidator<Customer> {
    public bool Validate(Customer t) {
        // validation logic
    }
}

Then, you could say:

Customer customer = // populate customer
var validator = new CustomerValidator();
if(!validator.Validate(customer)) {
    // head splode
}

This is the approach I prefer:

1. A Customer should not responsible for validating its own data, that is another responsibility and therefore should live elsewhere.
2. Different situations call for different validation logic for the same domain object.

What you have now are called "auto-properties," and only perform a simple "get/set". In order to customize the behavior of the get or set, you will need to convert the properties to field-backed properties:

private string _firstName;
public string FirstName 
{ 
    get {return _firstName;} 
    set 
    {
       Validate(value); _firstName = value;
    }
}

Note that I changed String to string and capitalized the property name, in following accepted C# naming best practices.

I wouldn't add validation in the setter at all. Rather, I would create a function called validate instead...that way all your validation code is in one spot rather scattered throughout your setters.