The name is a compound and it used to be a pair. Feng was the male bird and huang the female, and early sources treat them as two. By the imperial period the pair had collapsed into a single figure, and that figure had been assigned a gender: the fenghuang became female and was set opposite the long as the empress to the emperor. That is why the bird appears on bridal headdresses and on wedding textiles rather than on funerary goods.
The body is a deliberate composite. Descriptions assemble it from parts of other creatures, and the lists do not agree with each other, which is the point. A being made of everything belongs to no single species and can therefore stand for the whole ordered world. The tail feathers carry the five colours matched to the five virtues, so the bird is a moral diagram as much as an animal.
Its appearance is an omen and its absence is one too. Confucius is recorded lamenting that the phoenix has not come and the river has produced no chart, meaning that the age is out of order and no sage will be recognised in it. That reading, the bird as an index of good government, is what the fenghuang mostly does in the classical literature. The decorative use on porcelain, lacquer and embroidery comes later and carries the association without the argument.