How to tell Google that each subfolder is a different site? Otherwise, Google appends the main site's name to every other subfolder

Within another context I have given these examples of how to use hreflang and canonical links. For your purpose I added structural data in the head section of both examples with meta tags indicating an organization name, brand and department:

Example of an English webpage

http://example.com/en/

<!DOCTYPE html>
<html lang="en"> 
<head itemscope itemtype="http://schema.org/Organization">
     <title>English webpage</title>
     <meta content="My English Organization" itemprop="name">
     <meta content="My English Brand Name" itemprop="brand">
     <meta content="My English Department" itemprop="department">
     <link rel="canonical" href="http://example.com/en">
     <link rel="alternate" href="http://example.com/en/" hreflang="en">
     <link rel="alternate" href="http://example.com/nl/" hreflang="nl">
     <link rel="alternate" href="http://example.com/en/" hreflang="x-default">
</head>
<body>
     <p>This is a webpage written in English. 
        This page is also available in Dutch. 
        The default language of this page is English. 
</body>
</html>

Example of a Dutch webpage

http://example.com/nl/

<!DOCTYPE html>
<html lang="nl"> 
<head itemscope itemtype="http://schema.org/Organization">
     <title>Nederlandse webpagina</title> 
     <meta content="My Dutch Organization" itemprop="name">
     <meta content="My Dutch Brand Name" itemprop="brand">
     <meta content="My Dutch Department" itemprop="department">
     <link rel="canonical" href="http://example.com/nl" >
     <link rel="alternate" href="http://example.com/en/" hreflang="en">
     <link rel="alternate" href="http://example.com/nl/" hreflang="nl">
     <link rel="alternate" href="http://example.com/en/" hreflang="x-default">
</head>
<body>
     <p>Dit is een Nederlandstalige web pagina. 
        Deze pagina is beschikbaar in het Engels. 
        De standaardtaal van deze pagina is Engels.
</body>
</html>

This should be enough for Google to determine which page to use for a given locale. The canonical link is important.

Structured data could be used in the head section, although search engines may consume this data as they wish. In my examples I added a type 'Organization' in the head in microdata format, and some properties of this type: name, brand, and department. If have checked my examples using Google's Structured Data Testing Tool; in this way you can check the interpretation of your data. The result in GSDTT of the first example - which looks good to me - is:

@type Organization
 name My English Organization
 brand
    @type Thing
     name My English Brand Name
 department
    @type Organization
     name My English Department

It is up to you which properties from Organization you use. name seems most appropriate to me at first glance. You can find a full list of valid properties for this type at schema.org/Organization.

Additionally, I would recommend to create a sitemap, and update it when appropriate.

We checked today on November 29th and the title in the SERP no longer has the - Foobar USA appended to the end. It is now just Foobar Korea (not Foobar Korea - Foobar USA).

Here is what we did

October 27th (Day 0) - Added the following structured data:

<script type="application/ld+json">
{
"@context": "http://schema.org",
"@type": "Organization",
"url": "https://www.foobar.com/korea/",
"name": "Foobar Korea"
}
</script>

November 20th (Day 24) - Posted question here on Stack Exchange after no results.
November 24th (Day 28) - Our own research led us to add noodp <meta name="robots" content="noodp">. We are not sure if this really had any effect. It basically tells search engines not to use info from public directories as they may be outdated.
November 29th (Day 33) - Success! We checked Google SERP and the subfolder homepage www.foobar.com/korea/ no longer has the - Foobar USA appended to the end.

Extra notes

Even though we advised our client to annotate their pages with hreflang annotations, till this day, they have not yet done it. For the record, hreflang annotations was NOT used.
Title length was not changed. Page www.foobar.com/korea/ is still <title>Foobar Korea</title>.
No de-indexing and then re-indexing tactic was used.

It is quite difficult to determine the cause without examining the source code.

I assume that your website has errors with canonical meta links. Your web page for Korea www.foobar.com/korea/ should have <link rel="canonical" href="www.foobar.com/korea/foobar-korea.html" />.
If your website is multi-lingual then use meta hreflang.
Also check your code 301. Maybe there are mistakes.

Addition

The main question is how do we indicate to Google that each subfolder is a different organization.

7 Common Hreflang Mistakes (and How to Fix Them) + Bonus Tip:

Not Using Canonical Tags and Hreflang Tags Together Correctly. The hreflang tag also can be used along with rel="canonical" annotations, but hreflang tags need to reference self-referential canonical URLs. For example, page A should have a canonical tag pointing to page A, page B should have a canonical tag pointing to page B, and page C should have a canonical tag pointing to page C. All three pages should have hreflang tags that mention all three of the pages in the group. You do NOT want to canonicalize only one version of a page in a page grouping, as that would interfere with hreflang annotations.

Apply meta hreflang and canonical to USA:

<link rel="canonical" href="www.foobar.com/usa/main.html" />
<link rel="alternate" href="www.foobar.com/usa/main.html" hreflang="en-us" />
<link rel="alternate" href="www.foobar.com/korea/main.html" hreflang="ko" />

Apply meta hreflang and canonical to Korea:

<link rel="canonical" href="www.foobar.com/korea/main.html" />
<link rel="alternate" href="www.foobar.com/korea/main.html" hreflang="ko" />
<link rel="alternate" href="www.foobar.com/usa/main.html" hreflang="en-us" />

Read more: Lang unicode ++ Getting hreflang Right: Examples and Insights for International SEO (Moz) ++ Hreflang и Canonical International SEO Test.

Apply structured data - property Organization for United States:

<section vocab="http://schema.org/" typeof="Organization">
<h1 property="name">Name</h1>
<p property=areaServed>(The geographic area where a service or offered item is providedfor example:) Throughout on the United States</p>
<section property="address" typeof="PostalAddress">
<h2 property="name">Main address</h2>
<p property="streetAddress">Address</p>
<p property="postalCode">Code</p>
<p property="addressLocality">City</p>
<p>USA<meta property=addressCountry content=US /></p>
</section>

Apply structured data - property Organization for South Korea:

<section vocab="http://schema.org/" typeof="Organization">
<h1 property="name">Name</h1>
<p property=areaServed>(The geographic area where a service or offered item is providedfor example:) Throughout on the South Korea</p>
<section property="address" typeof="PostalAddress">
<h2 property="name">Main address</h2>
<p property="streetAddress">Address</p>
<p property="postalCode">Code</p>
<p property="addressLocality">City</p>
<p>South Korea<meta property=addressCountry content=KR /></p>
</section>

How to tell Google that each subfolder is a different site? Otherwise, Google appends the main site's name to every other subfolder

Here is what we did

Extra notes

Tags:

Internationalization

Seo

Title

Google Search

Serps

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