Heres one way you could do it (I am making a lot of assumptions, so the regexes will probably need tweaking):

use strict;
use warnings;

while ( <DATA> ) {
  #if it is in between the lines starting with name
  #and ending with a line of numbers and spaces 
  #note that the between in inclusive so it includes
  #those two lines.
  if ( /^name/ .. /^[\d ]+$/ ) {
    #don't want the next line of dashes or name line
    next if ( /name/ or /^---------------------------$/ );
    print $_;
  }

}

__DATA__
bunch
name
---------------------------
23 23 23 23 23 23 23 23 23
of
name
---------------------------
25 25 25 25 25 25 25 25 25
other
worthless
name
---------------------------
28 28 28 28 28 28 28 28 28
unnecessary and annoying
noise
1 2 3 4 9 8
name
---------------------------
29 29 29 29 29 29 29 29 29

__END__
23 23 23 23 23 23 23 23 23
25 25 25 25 25 25 25 25 25
28 28 28 28 28 28 28 28 28
29 29 29 29 29 29 29 29 29
[download]

-enlil