You can set the Maplex Label Engine to be as flexible or rigid as you need in placing labels relative to point features. You can specify a fixed distance that a label will be placed from a feature by defining an offset distance, or you can specify a maximum distance and allow labels to be placed within a range of acceptable distances. If you specify a maximum distance, the label is placed within that range and as close to the offset distance as possible. You can rotate point labels by an angle stored in an attribute or through an expression. The graticules of the map can also be used for point label alignment. You can also define preferred zones and blocked zones for label placement around the point feature.