Here's a breakdown:
* Nombre: Name
* Mi: My
* Hija: Daughter
* Grande: Eldest, big (in this context, it refers to age)
The phrase is a bit awkward in Spanish. It's more natural to say:
* El nombre de mi hija mayor (The name of my eldest daughter)
* Mi hija mayor se llama... (My eldest daughter is called...)
Let me know if you have any other Spanish phrases you'd like translated!