avoid using protected variable names in defining static pure functions

I will provide one example to show what the problem is.

Collatz[m_] := 
Collatz[m] = 1 + If[EvenQ[m], Collatz[m/2], Collatz[3 m + 1]];
Collatz[1] := 0;

this function works as expected but if I make a new function

myfunction[m_] := m

this generates and error

error: m is protected

I tried

f[# _] := #
f[4]

but the output is

f[4]

expected output is

4

I know I can use anonymous pure functions inline like

Function[#]&[arg]

but what if I want anonymous variable names that do not stay in memory? I want the function to be defined by name but I do not want to create more protected or reserved words inside the function arguments when I am defining the function. is there a way to use # or #_ to define a function without creating more protected variable names? is this possible in mathematica?