It seems like you're looking for something complicated when something simple will suffice. Why not just:

let foo = names.filter(name => name.length == 4 && /^j/.test(name));
let bar = names.filter(name => name.length == 3 && /^b/.test(name));

If you absolutely must do it in one pass I suppose you can use reduce, but dear god is it ugly:

let result = names.reduce((output, name) => {
    if(name.length == 4 && /^j/.test(name)) output[0].push(name);
    else if(name.length == 3 && /^b/.test(name)) output[1].push(name);
    return output;
  }, [[], []]);

Are you really telling me that's any easier to read than the first version? Even a simple straightforward for-each loop is easier to read than that mess. I think you should explain more the context of how this will be used.