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

[download]

In reply to Re: proper way of matching multiple line patterns by TJPride
in thread proper way of matching multiple line patterns by perlperlperl

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.