Can I compile a java file with a different name than the class?

To answer the question take a look at this example:
Create a file Sample.java

class A 
{ 
   public static void main(String args[])
   { 
      String str[] = {""}; 
      System.out.println("hi"); 
      B.main(str); 
   } 
} 
class B 
{ 
   public static void main(String args[]) 
   { 
     System.out.println("hello");
   }
} 

now you compile it as javac Sample.java and run as java A then output will be

hi 
hello

or you run as java B then output will be
hello

Notice that none of the classes are marked public therefore giving them default access. Files without any public classes have no file naming restrictions.

It is not necessary to name your file same as the name of the class it has, until this class is public. Though it is a good practice to name the file same as the name of class.

The compiler will compile your file successfully and make a dot class file. Now at the run time you need to give class name to the JVM for that you have to keep the name of the class, which has main method, in your mind. If you keep both the file name and the class name same, it will become easy to remember the name of the compiled dot class file.

for example:
file Dummy.java
class Dummy
{
   public static void main(String args[])
   {
    System.out.println("This is Dummy class running");
   }
}  

to run the above code we will use : 
 Javac Dummy.java // to compile
  Java Dummy   //to run

  example:
  file Dummy.java
class Diff
{
     public static void main(String args[])
     {
      System.out.println("This is Diff class running");
     }
}  

to run the above code we will use : 
Javac Dummy.java // to compile
Java Diff   //to run

yes, you can choose any name for the file (.java). there is no matter to what are the name of classes in that file means that class names may be totaly different from the file name. you should compile the program with file name and you should run the program with the class name in which the main method exist. main methods may be multiple in different classes so you should run it with the class name in which the main method you want to run......

By convention, the name of the main class should match the name of the file that holds the program. You should also make sure that the capitalization of the filename matches the class name.

The convention that filenames correspond to class names may seem arbitrary. However, this convention makes it easier to maintain and organize your programs. Furthermore, in some cases, it is required.

You can have your java file even without name ( simply ".java" ). Only thing is you should not have any public class in your file.