Learn English – Name for number format used in “Section 3.2.1”

I have always heard the "Sincerely, Joe Smith" part of a letter called the closing.

(And the part you describe as the greeting ("Dear Mr. Blahblah") I'm used to calling the salutation.)

In computing, LHS and RHS are sometimes used to mean the expressions on the left and right hand side of an operator.

Similarly, LValue and RValue are sometimes used for the expressions on the left and right hand side of an assignment operator (in particular because this places restrictions on the type of the lvalue, as it must be something that can be assigned to), but this is more specific to computing than to mathematics or other uses of such operators.

which are rarely used because order doesn't matter for those operations.

This is an influencing factor. All the terms you give in your question predate the formalising of the commutative property, which happened soon into the study of functions. As such, at about the same time that people first started to potentially care about grouping together the multiplier and the addend and so on, they also realised that they often don't care.

Also, why linguistically favour a given operand of an operator over a given term of an expression, when all single-operator expressions can be considered as a case of the wider set of expressions?