Actually, the names don't affect the classification at all - it does not matter how something is called, as it does not change its characteristics.
The classification of organism is based on their evolution and characteristics and it's a scientific consensus based on the data. Names don't impact it at all.
However, to increase understanding in science, scientist made the names after the place in the classification - so the scientific classification determines the names (but not the other way round).
Most offten you can tell how an animal is classified from the name, but only because it was named after this classification.