The perfect alignment of the sun,earth and moon causes a lunar eclipse. Is there such a thing as a full moon ?

Very good point & I agreed at first!

The visibly dark part of the so called "full" moon due to this effect would be at top or bottom of the disk (as observed from Earth) rather than to the left or right as it is when the moon is in a different phase.

EDIT (a few minutes later):

On further thought, it must be true that the sun lights more of the moon than is visible from Earth. This is because the size of the sun's diameter combined with its distance means that the sun's light is close to parallel and so reaches a full 50% of the moon's surface. By contrast, a human observer on Earth will be almost a point, and so the observer's lines of sight across the diameter of the moon will not be parallel. Thinking about this diagramatically it must be true that the observer will see less than 50% of the moon.

So, the dark part of the moon's disk which faces Earth may be invisible to the observing person standing on the Earth's surface. S/He will then see a true full moon.

The moon rotates the earth at an inclined angle of about 5 degrees, but this angle is enough so that when there is a full moon, it is an entire hemisphere of the moon you see.

The earth and moon do not rotate around the sun on a flat plane or else there would be eclipses constantly. But the moon being (almost) a sphere means that it is lit in a way that 50% of it is visible, but throughout the year a total of around 59% of the moon is lit the other 41% never seen from the surface of the earth.

A full moon relates to the amount of light showing on the surface of the moon relative to Earth. Half moon only has light on half it's surface. Full moon etc etc