In a word processing layout document (default), the first page is also a section. Additional pages are members of that section until you insert a new section. Presently, you have one document, one section, and multiple pages associated with that section.
To achieve a different first-page header, you would insert a new section, and in Page thumbnails, drag that new section icon before your existing section. Enter your first-page content in the header.
In the now second section, visit the Document > Section panel and deselect Match previous section. Your first section header is restricted to it, and you can now apply your name and page number to the second section header pages.