What is the type of each variable i.e. Categorical or Continuous? I have following attributes in my data-set.
Name, Date of Birth, Annual Income, Tax Paid, Gender.
What is the type of each variable i.e. Categorical or Continuous? and why ?

PS. I believe categorical attributes are the ones having fixed set of Values. Please let me know if I am wrong with this assumption. Also the "Name" attribute is just a label. but what category does it fall in ?
Name attribute cant be continuous, if you really want to use it then take it as a categorical. It depends on what is your use case.
Gender is categorical. 
Date of Birth/Annual Income/Tax Paid are in general continuous variable. But you may change them in categorical depending on your use case.