Paladins in 5e

What kind of restrictions should I use for 5e Paladins? Since there is no requirement from the rules should I match my Deity?

You should consider all aspects of your character In this edition. Specifically, look at what path you want to work and what build you will be taking. Consider your parentage, town of birth, temple practices, and deities's tenants. Only then should you decide how your Character responds to those teachings. Example: Tierna, a female Dragonborn Paladin of Bahamut is completely different depending on backstory and decisions. If she is an Orphan who is Oath of Devotion, taught to love and protect the weak no matter the means, Chaotic Good or Neutral good would be appropriate. If she is taught the strength of Bahamut, and how he defeats those that prey on the weak, she chooses Oath of Vengeance, a Lawful neutral is appropriate. If she secretly finds enjoyment from this destruction of life, justifying her acts because she only attacks "bad guys", she might even be Lawful Evil. There is no rule (In 5e), but you should think hard about your alignment, and discuss it with your DM at the game. 


In general, try to match at least 1 side of that gods' alignment, or consider a different god.