1) It may not be necessary to extract parts.

You can not use the linked parts instead?

2) If I understand you correctly, you should use the text insert {Part/Score Name}.

Do the following before you extract parts (or don’t extract; use the linked parts instead):

Enter on Page 2 a text block with the text insert Part/Score Name.

Give the text block the positioning you need (select the text block handle, and go to the text block’s Frame Attributes, e. g. via Shift-Return).

Also, in the Frame Attributes you can make the text block appear on a Page Range from Page 2 Through 0.

The zero will make the text block appear on Page 2 and onwards.

You may - in the very same text block - prefer to include other text, e. g. the text inserts {Title} and {Page Number}.

For the text block’s text, set font and size as needed.