The following table is an example how you should rename a font family:
For the legacy fields "Family Name" and "Subfamily Name" you should create a new family for each weight and subfamilies for each style (bold, italic, bold italic). For the newer "Preferred Family Name" and "Preferred Subfamily Name" you should create one family with a combination of weights and styles as subfamily. Start with the weight and add the style. Do not add a weight prefix for the default/regular weight. Create a new family for different widths (condensed), serife variants etc.