#!/usr/bin/perl

# create names lookup table from first file
while (<>) {
    #get rid of newline in name because there might be 
    #something like >name1\stext\n in the second file
    chomp;
    $names{$_} = 1;
    last if eof;
}
$/ = "\n>";  # set input record separator

# scan second file
print ">";            # print first ">" that would be missing
while (<>) {
      
    print if /^>?([\w\d]+)/ && $names{$1};
}