The issue arises when you don't have a trailing slash.
xyz.com/name/ with a trailing slash is conventionally a directory
xyz.com/name without a trailing slash is conventionally a file
Relative links from xyz.com/name will resolve relative to the root directory xyz.com/ because name is assumed to be a file within the root directory. This could break not only anchors but images and stylesheet links as well.
If name is a directory, some servers will automatically redirect to name/. Since yours doesn't, you could set it up to do so (either directly on the server via httpd.conf or via a .htaccess file in the root web directory.) This will prevent the aforementioned linking issues as well as prevent duplicate content from both URLs (an SEO concern.)
RewriteCond %{REQUEST_FILENAME} !-f 
RewriteRule ^(.*[^/])$ /$1/ [L,R=301]
More information and explanation can be found in the article "Should You Have a Trailing Slash at the End of URLs?" as well as by performing a web search for trailing slash in URL.
An alternative to redirecting is to use the <base> HTML element in the <head>, which specifies the base URL to use for all relative URLs in a document.
Caution: this can break in-page anchors. Using <base href="/name/"> on xyz.com/name/other.html, the link <a href="#some-id">in-page anchor</a> points to xyz.com/name/#some-id. However, it's not necessary to use <base> in every page, only in index.html.