Making a Will is not about wealth it is about making sure that what you want to happen to your estate does happen. It gives you the opportunity to specify such things as who will administer your estate, who will care for your children and who will receive specific items of your property.
You should state your full name and any other name by which you are commonly known. This sounds obvious but is a point often overlooked.
If you have a name which can be spelt several ways it is quite possible that you have assets in more than one spelling.
You may also have a middle name used only infrequently so that your bank account is in one name but your birth (and thus death) certificate says your full name.
These matters can be dealt with at the probate stage but if you are commonly known by a name other than your given name it is best to include it in your will. For example, 'I John Brown otherwise known as Jack Brown'.