How to match a hash string generated from SHA512 algorithm to payment gateway string

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C#

I am integrating my asp .net web application with a payment gateway and in their documentaion they told to use the SHA512 algorithm for a string.
so i am using the SHA512 hash code as shown below and genrating the hash signature.
But the signature i am generating is different from their. SO i am getting an error.

So the question is

1) all the SHA512 algorithms produce same output?
Im my search they are not same
2) If there are many SHA512 algorithms then which one i want to use?
Can i ask the payment gateway people for the algorithm?
3) Is there any generic SHA512 algorithm that matches with all the remaining algorithms?

I am sorry if these questions seems to be funny. But i am new to this payment gateway integration.

Thanks in Advance

What I have tried:

public String computeHash(String message)
{
byte[] sourceBytes = Encoding.Default.GetBytes(message);
byte[] hashBytes = null;

hashBytes = SHA512Managed.Create().ComputeHash(sourceBytes);

StringBuilder sb = new StringBuilder();
for (int i = 0; i<hashBytes.Length; i++)
{
sb.AppendFormat("{0:x2}", hashBytes[i]);
}
return sb.ToString();
}