There are many ways to do this.  Here's one suggestion:

my %out;
while (<DATA>) {
    chomp;
    my ($id, $name) = split ' ', $_, 2;  # split line into two parts
    ($id) = $id =~ /^([^.]+)/;           # extract "name1", "name2" as
+ $id
    $out{$id} .= " $name";               # assemble stuff by $id (in a
+ hash)
}

for my $id (sort keys %out) {
    print $id, $out{$id}, "\n";
}

__DATA__
name1 TOM RAT
name1.1 AND
name1.1.1 JERRY
name2 BAT MAN
name2.1 CAN
name2.1.1 FLY
name2.1.2 ANYWHERE
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(feel free to ask if you need more detailed explanations)