abaugher@bannor:~/work/perl/monks$ cat 939472.pl
#!/usr/bin/perl
use Modern::Perl;

open my $in, '<', '939472.txt' or die $!;

my $n = 0; # current number

while(my $line = <$in>){
    chomp $line;
           # capture any digits directly following 'name'
           # and the text following the first space
    my( $nn, $text ) = $line =~ /name(\d+)\S*\s+(.+)$/;
    if( $nn == $n ){      # already working on this name?
        print " $text";   # if so, then print what we've got
    } else {
                                     # if not, start a new line
        print "\n" unless $n == 0;   # unless this is the first line
        print "name$nn $text";       # print the new number and text
        $n = $nn;                    # and update the name counter
    }
}
print "\n";

abaugher@bannor:~/work/perl/monks$ cat 939472.txt
name1 TOM RAT
name1.1 AND
name1.1.1 JERRY
name2 BAT MAN
name2.1 CAN
name2.1.1 FLY
name2.1.2 ANYWHERE

abaugher@bannor:~/work/perl/monks$ perl 939472.pl
name1 TOM RAT AND JERRY
name2 BAT MAN CAN FLY ANYWHERE