With the introduction of C# 6 (in VS 2015), you can now have get-only automatic properties, in which the implicit backing field is readonly (i.e. values can be assigned in the constructor but not elsewhere):
public string Name { get; }
public Customer(string name) // Constructor
{
Name = name;
}
private void SomeFunction()
{
Name = "Something Else"; // Compile-time error
}
And you can now also initialise properties (with or without a setter) inline:
public string Name { get; } = "Boris";
Referring back to the question, this gives you the advantages of option 2 (public member is a property, not a field) with the brevity of option 1.
Unfortunately, it doesn't provide a guarantee of immutability at the level of the public interface (as in @CodesInChaos's point about self-documentation), because to a consumer of the class, having no setter is indistinguishable from having a private setter.