Can 2 people in the same house claim earned income ?

It depends.  

If you are living with someone and NOT married to them and neither person claims the other person as a dependent on their return, if you both qualify for the Earned income credit, then Yes, you can both claim it.  Another person in your home that is not in your tax family does not affect your ability to claim the Earned Income Tax Credit. 

If you are married then you would need to file a joint return in order to claim the Earned Income Tax Credit.  

If you are married and file separately, then NO, you cannot claim the EITC.  You must file jointly in order to claim the credit. 

If someone is claiming you as a dependent on their return, you cannot claim the Earned Income Tax Credit.