Orbital period only depends on an orbit's semi-major axis and the mass of the more massive body, which means that different orbits around a planet or moon have the same period as long as the orbits have the same width at their widest point.
Here are a few orbits with different eccentricities but the same semi-major axis, aligned to have their periapses on the same side:
Drawing more eccentricities makes it harder to distinguish one orbit from another, but it does produce a memorable teardrop shape: