Is the following the correct way to "map" how a lambda function looks to how it would be written in scheme?
(λx.x+1) 5 ↦ (lambda (x) (+ x 1) 5)
Additionally, how are lambda functions 'named' in the formal notation? Is there something that corresponds to this:
Add One = (λx.x+1)
(λx.x+1)5 is an application to the argument 5. In Scheme code this would be equivalent to:
((lambda (x) (+ x 1)) 5)
Here the (lambda (x) (+ x 1)) constitutes the function, and it must be placed in a function call context by wrapping it in parentheses with its arguments.
As far as naming in formal notation is concerned, this is not a feature of the lambda calculus proper. In texts it is often found that some sort of identifier notation is used to facilitate the expression of combinations; it seems like very simple identifiers are usually preferred in these cases. This is really mathematical notation, not programming notation. I have seen both of these:
A ≡ λx.x+1
A = λx.x+1