New variants are not named by the media as you imply. Variants are named following a convention discussed
here and
here by the WHO. Mutations are only part of the story as "variants of concern" are defined based on phenotypic effects such as increased changes to their tranmissibility and virulence, and decrease effectiveness of vaccines to combat them; they are not named solely due to novel mutations in residues; this is because not all mutations result in changes in transmissibility, virulence, and vaccine efficacy. That viruses mutate is trivially true and recognized by all. It depends on where the mutations occur in the 29 proteins that comprise the virus with respect to their epidemiological consequences.
(new flu strains do get named by the CDC)