Whether you have one savings account or several is more of a person choice. I used to have multiple ones thinking I would have each account as a separate savings goal but eventually I ended up not using them and consolidated it into one. It depends more on what you are saving for and how organised you are.
What are your goals?
The first question you need to ask is what are you saving for. You should set up an emergency fund which has enough money in it to cover unexpected expenses. If you then have other things to save for like a holiday or Christmas you might want to open up separate accounts. Keep your emergency fund separate so that you do not accidently dip into the needed funds.
Track your progress
Once you have your emergency fund set up you can look at how many others you might want. An advantage of having separate accounts is that you can track your progress of reaching your separate savings goals. For me personally I would find this easier if all my savings accounts were in the same place and I could view them together through online banking.
Organises your budget
Having separate accounts can help you organise your budget because you can see exactly how much you need to put in each week/fortnight/month over your year. You may need to make some changes to your budget if you are adding another account or upping the amounts.
Are you organised
A disadvantage with having multiple accounts is that it can get quite confusing and you need to be organised. Some people also might get deterred by only small amounts spread over many places, and some may be more motivated by putting their money into one account and seeing the savings build more rapidly. If you are a bit disorganised you may find it easier to set up direct debits from your transaction account into your different savings accounts.
Where are you going to put them?
If you are going to utilise multiple accounts you need to explore where you are going to put them. Try and find accounts with the highest interest rates (usually online accounts). I found when I had my online account with the same bank as my transaction account it was easier to dip into my savings, so you might want to consider having them in a separate place.
There are constantly different deals going by the banks to try and entice you to join (often coming with special interest rates). There is no harm changing them around as these do not affect your credit rating.
What about fees
Do look at the type of account you are opening. There are sometimes differences in accounts where you may need to deposit a minimum monthly amount and make no withdrawals to earn any interest. I used to find when I worked in the branch that many customers did not know the features of their accounts.
Once they went over one withdrawal not only did they not earn interest but they started getting charged. Make sure you know the conditions of the accounts and any fees and charges you may get.