Cominarty is the brand name for the Pfizer-Biontech COVID mRNA vaccine.
Under EUA, drugs/vaccines are not allowed to be marketed so it was not "branded or licensed" ( ie It hadn't been given a legal name...at least not publicly).
We've used the manufacturers name to identify all the COVID vaccines while under EUA. That allowed identification of specific vaccines especially between the different mRNA vaccines. Once it had full FDA approve, the branded/licensed name was used. All vaccines have a brand name. We just don't use those names outside of health facilities. We just say flu shot/jab (there's actually about 10 different ones).
You'll see similar with Moderna and J&J when they get full approval.
Link to facts (Cominarty website)
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Another link to facts (FDA)
On August 23, 2021, the FDA approved the first COVID-19 vaccine. The vaccine has been known as the Pfizer-BioNTech COVID-19 Vaccine, and will now be marketed as Comirnaty, for the prevention of COVID-19 disease in individuals 16 years of age and older.