No you don't HAVE to, but keep in mind, you are trying to prove your relationship is genuine. If you and your spouse come from backgrounds that have a high expectation that you are to take on your spouse's name, and you haven't, then immigration may question that... however keep in mind in many places here in Canada it is quite normal for spouses to keep their own names... If this is a concern for you, you could (like me) change a few items of ID to show that you are in the process of changing everything over and CIC will see your intent. If you are not concerned, then don't worry about it.
Make sure you submit all forms that prove your previous marriage is annulled/divorced. The definitely need to see that proof.
Also, if you have any kind of joint accounts with your present husband then show that. Even though my husband and I are in separate countries right now and have never lived together officially... I was able to add him to my health benefits program at work of which they issued him a document for so I submitted a copy of that... You need to show that your marriage is GENUINE and CONTINUING... Costco allows you to sign up for membership for yourself and a your spouse even though they are not in Canada at this time.. they will issue you both a card but his will only have his name and no photo... if you dont already have an account they are $55, if you do, go add his name and get his card and submit a copy with your app... Little things like that can help prove you plan to cohabit together as husband and wife etc... If you can put things into perspective like that and submit proofs showing it, then you will make your app stronger.
As much as you have to focus on proving your future, you also have to focus on proving your past. Try and step out of the box and look at your relationship on paper. Write out a timeline if it helps. Things that may be obvious to you, may not be so obvious to a stranger. Your Immigration officer is a STRANGER to you. Remember that. They are paid to be skeptical of all applications and not to assume that everyone is genuine.
Take time with your application. Don't rush it, dont leave anything out... this whole process is one big waiting game and it starts with your application. Use this forum to your advantage. There are lots of very knowledgeable people on here that are willing to help. Ask questions. Find the Phillipines thread and introduce yourself. Remember, you are not alone!
I wish you all the best!