lookup with multiple conditions (AND and OR)

I need to create a lookup in a table where I need to match one value in one column and another value in one of two columns (boolean: A * (B+C)). I have tried to attached an example.

I have tried using an INDEX MATCH formula, which works, unless the client name is not unique.

Any idea how I can do this, so it will work with not unique names? (The combination of name and item is always unique)