Stop thinking of “variables”- all values in Elixir are immutable. However identifiers can be rebound to new values. So the only thing that can “vary” is the value the identifier is bound to - not the value itself.
Imperative languages are about PLace-Oriented Programming (PLOP) - in functional programming you are programming with values (The Value of Values).

Furthermore you don’t “loop” in Elixir - you recurse.

I suggest using if else for this. Also, to mutate your map you have to use explicit assignment, so my_map = if (...).

Oh, and in Elixir snake_case is the most widely used convention.

Check out Enum.reduce

defmodule Demo do

  def replace_with(list, value) do
    fn {x , _} = pair ->
      cond do
        Enum.member?(list, x) -> {x, value}
        true -> pair
      end
    end
  end

end

myOtherList = ["b"]
myMap = %{"a" => "no", "b" => "no", "c" => "no"}

newMap =
  myMap
  |> Enum.map(Demo.replace_with(myOtherList, "yes"))
  |> Map.new()

IO.inspect(newMap)

$ elixir demo.exs
%{"a" => "no", "b" => "yes", "c" => "no"}
$

Will myList always be identical to Map.keys(myMap)? Or will they diverge?

Will Map.values(myMap) always be identical to a list of "no"? Or might there be other values?

In the following solution, I will assume, that myList and Map.keys(myMap) might be different, while the values all have to be "no".

intersection_of_keys = myList -- myOtherList

for {k, v} <- myMap, into: %{} do
  if k in intersection_of_keys, do: {k, "yes"}, else: {k, "no"}
end

The reason why your original code did not work is, because the inner binding in the fn you pass to Enum.each/2 does not change the outer binding of myMap, always remember, elixir is immutable, it does only support shadowing, but shadowing does never leak its scope.