One possible way:

c:\@Work\Perl>perl -wMstrict -MData::Dump -le
"my $s = q{name1=value1 name2=' value2=0' name3=value3};
 ;;
 my $name     = qr{ \w+ }xms;
 my $plain    = qr{ \w+ }xms;
 my $s_quoted = qr{ ' [^\x27]* ' }xms;
 ;;
 my %h = $s =~ m{ ($name) \s* = \s* ($s_quoted | $plain) \s* }xmsg;
 dd \%h;
"
{ name1 => "value1", name2 => "' value2=0'", name3 => "value3" }
[download]

Please see perlre, perlrequick, and perlretut.

Updates:

1. Note that  \x27 in  [^\x27] represents a  ' (single-quote) character. I have to use this form because my REPL does not like unbalanced single-quotes in a command-line code expression. You can use  [^'] like a sane person.
2. Another and probably better approach would be to forget regexes and use Text::CSV or Text::CSV_XS.
3. If you need to get rid of the single-quotes and have Perl version 5.10+, try this. Note that  $s_quoted is changed and the  m// match uses  (?|pattern) from Extended Patterns.

   c:\@Work\Perl>perl -wMstrict -MData::Dump -le
   "use 5.010;
    ;;
    my $s = q{name1=value1 name2=' value2=0' name3=value3};
    ;;
    my $name     = qr{ \w+ }xms;
    my $plain    = qr{ \w+ }xms;
    my $s_quoted = qr{ [^\x27]* }xms;
    ;;
    my %h = $s =~ m{ ($name) \s* = \s* (?| ' ($s_quoted) ' | ($plain)) \s
   +* }xmsg;
    dd \%h;
   "
   { name1 => "value1", name2 => " value2=0", name3 => "value3" }
   [download]

   If you don't have 5.10, let me know. There's a simple alternative.