You're pretty close. In a scalar context a regex returns the number of matches. In a list context, it returns the list of matches.

my ($info_name) = $line =~ /\<info_name\>(\S+)\<\/info_name\>/i;

And now for some notes...

• DON'T DO THAT! Using regexs on XML is fragile.
• Use something like XML::LibXML
• I see fasta in there so you may like Perl and Bioinformatics
• use strict;
• use warnings;
• XML element names should always be lower case, so you don't need to ignore the case in your regex.
• Your example XML has 3 copies of the same structure so you will end up with one unique key in your hash.
• Unless this is the beginning of nested t_volumes, you missed the / in </t_volume>

For my example, I decided to rely on the fact that the interesting tags do not contain other tags. If that changes, my code breaks. I also rely on the order of the tags as shown in the example XML, which is generally a dumb assumption since things like XML::LibXML can reorder the elements.

#!/usr/bin/perl
use strict;
use warnings;

my @files = glob('./*.xml');

my %results;

foreach my $xmlname (@files) {
    open my $fh, '<', $xmlname or die "$xmlname: $!";
    
    while ( my $line = <$fh> ) {
        my ($name) = $line =~ /\<info_name\>([^<]+)\<\/info_name\>/
            or next;
        while ( my $l = <$fh> ) {
            $l =~ /\<it_size\>([^<]+)\<\/it_size\>/ or next;
            $results{$name} = $1;
            last;
        }
    }
}

print map { "$_ => $results{$_}\n" } keys %results;
[download]

jth@reina:~/tmp$ perl 848551.pl 
FZGA34177.b1 => 35000
[download]

And finally, my XML::LibXML alternative which does not rely on tag ordering or the content of the tag.

#!/usr/bin/perl
use strict;
use warnings;
use XML::LibXML;


my @files = glob('./*.xml');

my %results;

foreach my $xmlname (@files) {
    my $dom = XML::LibXML->load_xml(
        location => $xmlname,
        recover => 1, # no </t_volume> in example
    ) or die $!;
    
    foreach my $node ( $dom->findnodes('//info') ) {
        $results{ $node->find('info_name') } = $node->find('it_size');
    }
}

print map { "$_ => $results{$_}\n" } keys %results;
[download]

jth@reina:~/tmp$ perl 848551.pl 
./848551.xml:55: parser error : Premature end of data in tag t_volume 
+line 54

^
./848551.xml:55: parser error : Premature end of data in tag t_volume 
+line 2

^
FZGA34177.b1 => 35000
[download]