Customizing name associated with device in group

I recently bought an iPhone 12 and gave my iPhone 8 to my wife to use. The problem is this: She is complaining because when she texts someone on her device it uses my name and people on the receiving end think that it’s me instead of her. When she changes the name to her name on her device it then changes the name on my device. We don’t mind the devices joined together except it would be better if we could keep a separate name associated with each device. Can this be done easily?