If it is the same name that you are looking for each time and you want to
delete all of the pages on which that name appears, the following macro will
ask you for the name and then do it all for you:

Dim findname As String, namepage As Range
findname = InputBox("Enter the Name that you are looking for.", "Page
Deleter")
Selection.HomeKey wdStory
Selection.Find.ClearFormatting
With Selection.Find
   Do While .Execute(FindText:=findname, Wrap:=wdFindContinue,
Forward:=True) = True
       Set namepage = Selection.Range.Bookmarks("\page").Range
       namepage.Delete
   Loop
End With

Andrea,

And for "why": Word changes from searching "all" to "down" if you have
something selected before you start the search.

In that case, Word initially only searches the selection. When it has
finished, it'll ask you whether it should search the rest of the document.

BTW, nice keyboard shortcuts to find the next/previous occurrence without
opening the dialog again are Ctrl+PageDown ( = BrowseNext)  and Ctrl+PageUp
(= BrowsePrevious).
The blue double arrows below the vertical scoll bar (to the right of the
document) serve the same purpose if you prefer the mouse.

Regards,
Klaus