Yes, marettes (wire nuts) are the standard way of bundling the wire ends as discussed here.
They come in different sizes for the number and size of wires to be joined.
Two wires under one screw are permitted only when the screw terminal is designed for that purpose; where there are grooves or a cap piece that hold both wires in place not curled and not criss crossing, and they can't slip out sideways even partially just before the screw is tightened.
Where you could attach both wires directly to the device (receptacle, etc.) and by fielders choice or otherwse connected the incoming and continuing hots directly to each other with a pigtail, then you must pigtail the neutral similarly. It isn't good to find the hot still connected downstream and the neutral path broken for any length of time if you were doing some maintenance and uninstalled the receptacle. The neutral throughout the downstream portion of the circuit would be live if you turned the power on before finishing the job and something downstream was switched on. And you could be confused since the item you switched on would not work without the neutral path re-completed.