You may be overthinking this. Records are probably not going to be more than like 100-150 characters, so unless you have hundreds of thousands of records, you're not likely to run into memory problems. But yes, as other people have mentioned, you can set the line separator to Name, like so:

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

my $first = 'Name';   # Name of first field in each record
my %data;

$/ = "$first: ";
<DATA>;
while (<DATA>) {
    chomp; $_ = $/ . $_;
    %data = ();
    $data{$1} = $2 while m/^(.*?): (.*?)$/mg;
    print Dumper(\%data);
}

__DATA__
Name: Theodore Pride
Phone: (911) 911-9111
Address: 1234 Road
Name: Theodore Pride
Phone: (911) 911-9111
Address: 1234 Road
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