Error: Could not find or load main class with OpenJDK and Oracle Java on CentOS 7

On CentOS 7.2 Linux I have successfully downloaded and installed Oracle Java with:

# rpm -Uvh jdk-8u91-linux-x64.rpm

Also there is already OpenJDK installed:

# rpm -qa | grep -i jdk
java-1.8.0-openjdk-headless-1.8.0.91-0.b14.el7_2.x86_64
java-1.8.0-openjdk-1.8.0.91-0.b14.el7_2.x86_64
jdk1.8.0_91-1.8.0_91-fcs.x86_64

I can switch between the 2 using this command:

# alteatives --config java

There are 2 programs which provide 'java'.

  Selection    Command
-----------------------------------------------
*  1 /usr/lib/jvm/java-1.8.0-openjdk-1.8.0.91-0.b14.el7_2.x86_64/jre/bin/java
 + 2 /usr/java/jdk1.8.0_91/jre/bin/java

Enter to keep the current selection[+], or type selection number:

And see the version with:

# java -version
java version "1.8.0_91"
Java(TM) SE Runtime Environment (build 1.8.0_91-b14)
Java HotSpot(TM) 64-Bit Server VM (build 25.91-b14, mixed mode)

# javac -version
javac 1.8.0_91

Now to my problem please -

I create a simple java file named TheClassName.java:

package thepackagename;

public class TheClassName {
        public static final void main(String[] args)  {
                System.out.println("Hello World!");
        }
}

After successfully compiling it with javac TheClassName.java (which produces TheClassName.class file in the same dir) I unfortunately can not run it:

# java -cp . thepackagename.TheClassName
Error: Could not find or load main class thepackagename.TheClassName

Here another try:

# export JAVA_HOME=/usr/lib/jvm/java-1.8.0-openjdk-1.8.0.91-0.b14.el7_2.x86_64/jre
# $JAVA_HOME/bin/java -cp . thepackagename.TheClassName
Error: Could not find or load main class thepackagename.TheClassName

Setting another environment variable does not help either:

# export CLASSPATH=.

Similar command on Windows 7 works well and I have tried copying the TheClassName.class file from there to Linux too.

Please help and please do not suggest marking this question as duplicate, because as you see above, I have already tried most of the suggestions.

The SELINUX is off (SELINUX=disabled) and the server was installed few weeks ago, serving (without errors) as LAMP with MySQL/PostgreSQL/Apache/Wordpress.

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