Lets say I have a class Size.
With the mutable version it feels natural to go
size.add(2);
But the immutable feels better like this
newSize = size.plus(2);
I'm fairly new to immutable objects. What is the naming convention for this and other methods?
That is asking for opinions, not for facts.
You can let yourself be guided by the BigDecimal class for the naming convention:
http://docs.oracle.com/javase/7/docs/api/java/math/BigDecimal.html
But if you want to use "plus" in stead of "add" - why not? Its your code and if you find that readable then just do it.
EDIT: please be aware that I did not notice your stackoverflow history before giving this answer. I would have probably chosen to shut up if I had noticed you are not a novice :)