I would recommend to first read all of your data into a datastructure, like a hash of hashrefs with the names as the keys and then process the data according to your logic:

use strict;
use warnings;
use Data::Dumper;

my @extract;
while(<DATA>){
if /^\.EON/ or /^\s*$/;
        push @extract, {name => $1} and next if /^\$ NAME : (\w+)/;
        ${$extract[-1]}{$1} = $2             if /(\S+)\s*(.*)/;
}

my %result = map { delete $_->{name} => $_ } @extract;

print Dumper \%result;

__DATA__
$ NAME : corry   
$$.Inc s d  
$$.Oc s 
$$.TO

G1 ty n1 EE EE M T1 T2 $$SRU   
G2 n1 y OO OO M T3 T4 $$SRU   
.EON  

$ NAME : patrick  
$$.Inc c d
$$.Oc c 
$$.TO 

G1 td n3 EE EE M T5 T6 $$SRU    
G2 n3 y OO OO M T7 T8 $$SRU  
.EON 

$ NAME : sandy    
$$.Inc k l
$$.Oc l
$$.TO

G1 td n3 FF FF M R5 R6 $$SRU      
G2 n3 y OO OO N R7 R8 $$SRU    
.EON
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