I updated your code a bit. You are now able to Type 15F, 15C, ... (without whitespace) to convert. After this you will be asked if you want to continue.

public static void main(String[] args) {
        double deg = 0;
        Scanner input = new Scanner(System.in);

        do {
            System.out
                    .println("Enter a number and F to convert from degF to degC or C to convert to degC to degF");
            String text = input.next().toUpperCase();

            try {
                deg = Double.parseDouble(text.substring(0, text.length() - 1));
            } catch (NumberFormatException e) {
                e.printStackTrace();
            }

            if (text.endsWith("C")) {
                double cTemp = (deg - 32) * 5.0 / 9.0;
                System.out.printf("%f degC converted to degF is %.2f%n", deg, cTemp);
                ;
            } else if (text.endsWith("F")) {
                double fTemp = (deg * 9 / 5) + 32;
                System.out.printf("%f degF converted to degC is %.2f%n", deg, fTemp);
                continue;
            } else {
                System.out
                        .println("That character does not correspond to a valid unit of measure ");
            }
            System.out.println("Type YES to continue");
        } while (input.next().equalsIgnoreCase("YES"));
        input.close();

    }

1. If you don't use Java 7 you can't use switch-strings

2. Change while (true) with while (yn) so it will stop when he type "no", and change boolean yn; to boolean yn = true; And change the rules inside the cases too.

   case "yes":
        yn = false;
        break;
   case "no": 
        yn = true;
        break;
   

   yn = true; if "yes";

   yn = false; if "no";

   You could change the condition inside the while, with while (!yn) but is more intuitive to let yn true if yes; false if no.

3. return default; don't make much sense, if you want to let user repeat in case of error well.. you should do a new while (true) to repeat until he writes a correct one. I would write another method.

This is how you could do it

Scanner kbd = new Scanner (System.in);

String decision;

boolean yn = true;
while(yn)
{
    System.out.println("please enter your name");
    String name = kbd.nextLine();

    System.out.println("you entered the name" + name );

    System.out.println("enter another name : yes or no");
    decision = kbd.nextLine();


    switch(decision)
    {
        case "yes":
            yn = true;
            break;

        case "no":
            yn = false;
            break;

        default:
            System.out.println("please enter again ");
            boolean repeat = true;

            while (repeat)
            {
                System.out.println("enter another name : yes or no");
                decision = kbd.nextLine();

                switch (decision)
                {
                    case "yes":
                        yn = true;
                        repeat = false;
                        break;

                    case "no":
                        yn = repeat = false;
                        break;
                    default:
                        repeat = true;
                }
            }
            break;
    }
}

Yes it will repeat decision code, but how it is created i think it is the only way to do it.

Please, read and follow the Posting rules and also the Code Posting rules.

You keep making low effort, code only posts that are not even properly formatted. This behavior is unacceptable when asking for help.

The Posting Rules mentioned above explain how a proper post needs to be made. The Code posting rules explain how to post code.

Since this is not the first time you do this, consider it a warning. Further similar behavior will lead to consequences such as a permanent or temporary ban from this subreddit.

Your code only checks the first character of the input, so it's no wonder words starting with y or n are considered valid. You might want to compare the entire String :

String response = keyboard.next();
while (!response.equalsIgnoreCase("y") && !response.equalsIgnoreCase("n")) {
  System.out.println("\nInvalid response. Try again.");
  response = keyboard.next();
} 
if (response.equalsIgnoreCase("n")) {
  System.out.println("\nCome back next time, " + customerName + ".");
} else {
  System.out.println("\nGreat! Let's get started.");
}