In the "Miraculous: Tales of Ladybug & Cat Noir" series, Ladybug does not transform into Lady Noir after Hawkmoth receives Cat Noir's Miraculous. Instead, Lady Noir is a separate character and transformation. When Hawkmoth (Gabriel Agreste) temporarily controls Cat Noir's Miraculous, he uses it to create various akumatized villains, but he does not transform into Lady Noir.
Ladybug and Cat Noir are distinct superhero identities that the main characters Marinette Dupain-Cheng and Adrien Agreste take on, each with their own specific Miraculous. The dynamic between them remains central to the plot, with unique transformations, powers, and responsibilities. If you have any more questions about the series, feel free to ask!