SSL on Server

Hi,
I Got Issued A SSL certificate for mySite www.xyz.com as
ISSUED to SSL on Serverecure.xyz.com. the Thing is That It is running fine on www.xyz.com. Like I can use the same Pages As on http:// and https://

Do i need to ask Verisign to Change the Certificate to www.xyz.com or Stick with this one?.

One more thing Will it Effect my Checkout System With verisign ?

 

 

 

 

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