The serialized objects are stored in the file "nameStore", like the code specifies. Where that file is created depends on what the default directory is when this code is run. If you want control over the directory, use absolute paths instead of relative paths.
serialization is volatile, like until and unless program shutdown serialization works after that it'll not right?
I'm not sure what you're trying to say here, but serialization is frequently used to store data for later use during a future invocation of the JVM. So I think your understanding is wrong.
Personally, I don't like to use binary serialization, I prefer XML serialization using the java.beans.XMLEncoder and XMLDecoder classes. For storing game status it should be easy to meet the requirement that the serialized classes obey JavaBeans conventions.
You should also check out the java.util.prefs package. For a desktop app that may be a better fit than serialization - for example, you don't have to worry about files, and where they might get stored.