The term deadname refers to the name given at birth to a transgender/nonbinary/genderfluid person who has chosen a different name. Even if the person's legal name is their birth name (i.e. they have not had it legally changed), it is still considered a deadname if they prefer to be called something else.
The verb deadnaming is the act of referring to a trans/nonbinary person by their birth name, which is almost universally considered offensive. Deadnaming can cause gender dysphoria, and can out the person being deadnamed, possibly causing further harassment and discrimination.