Too long for comment
In general: a server has a hostname, such as example.com , not a URI that includes both a hostname and directory path such as example.com/name.
Now there can be a mapping that maps a particular directory path from the server that hosts example.com to a different (back-end) server. That is usually called a reverse proxy (although some appliances/tools implement such mappings slightly differently).
It sounds like your server is the back-end server, let's call that name.internal.example.com.
It is the responsibility of whomever manages example.com to ensure that http(s)://example.com/name/ with a trailing / is mapped the same as http(s)://example.com/name without a trailing /.
Generally it will help when you deploy your content in the same directory that the front-end uses for your content, i.e. in the directory /name
Then http(s)://example.com/name can be mapped to http(s)://name.internal.example.com/name (note that both omit the trailing forward slash) - That usually ensures that when requests such as http(s)://example.com/name/ http(s)://example.com/name/path/to/some/content will also be mapped correctly to your back-end server.
Typically that requires no particular complicated configuration in your apache back-end server. A minimal VitrtualHost block like:
<VirtualHost *:80>
ServerName name.internal.example.com
DocumentRoot "/var/www/html"
</VirtualHost>
and publish your web content in the directory /var/www/html/name
