1) Is it true that if we use a middle name when naming a child, the child must always be addressed using that middle name? Please provide necessary evidence.
2) Which name is more correct if naming after the daughter of Nabi SAW, Fathimah or Fathimah Zahra?
In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
1) Your question is not clear. In principle, a child may be called by whatever name he/she has been given as long as the names have good meanings and are accepted in shariah.
2) Fatima: (name of the daughter of Rasulullah Salallahu Alayhi Wasallam)
Zahra: (radiant) which was a title given to the daughter of Rasulullah Salallahu Alayhi Wasallam. 
Hence, one may keep the name Fatimah, Zahra or Fatima-Zahra.
And Allah Ta’āla Knows Best
Student Darul Iftaa
Checked and Approved by,
Mufti Ebrahim Desai.