The asymmetric atom is called a chirality center, a type of stereocenter. A chirality center is also called a chiral center or an asymmetric center. Some sources use the terms stereocenter, stereogenic center, stereogenic atom or stereogen to refer exclusively to a chirality center, while others use the terms more broadly to refer also to centers that result in diastereomers (stereoisomers that are not enantiomers).
Compounds that contain exactly one (or any odd number) of asymmetric atoms are always chiral. However, compounds that contain an even number of asymmetric atoms sometimes lack chirality because they are arranged in mirror-symmetric pairs, and are known as meso compounds. For instance, meso tartaric acid (shown on the right) has two asymmetric carbon atoms, but it does not exhibit enantiomerism because there is a  mirror symmetry plane. Conversely, there exist forms of chirality that do not require asymmetric atoms, such as axial, planar, and helical chirality.
Even though a chiral molecule lacks reflection (C) and rotoreflection symmetries (S), it can have other molecular symmetries, and its symmetry is described by one of the chiral point groups: C, D,  T, O, or I. For example, hydrogen peroxide is chiral and has C (two-fold rotational) symmetry. A common chiral case is the point group C, meaning no symmetries, which is the case for lactic acid.