Name = (1) a word or a combination of words by which someone or something is designated, called, or known: ‘I refused to give them my name.’ (2) a person’s reputation: ‘He wanted to protect his good name.’ (3) family name based on male descent: ‘He had no sons and there was no one to carry on his name.’ (4) a well-known or notable person: ‘They studied all the great names in the history of France.’
When you mention the name by which someone or something is known, use call/be called (NOT name/be named): ‘Most people call him Bob but he prefers to be called Robert.’
Name a child after sb: ‘We’ve decided to name her Sarah, after her grandmother.’