What symbol does the goddess Isis need?

In a way, yes she did. This was the side view of a throne - which was part of her name written in hieroglyphs - often shown carried on her head. Just as often she is shown with cow horns and a sun disk on her head, but this is also sometimes worn by Hathor.

On its own, however, the side view of throne is simply the hieroglyph for "throne" and does not itself mean Isis. Only when shown on the head of the goddess, or in close association with her, is it the symbol of Isis.

See link below for an images: