Trouble looms in Elon Musk's household as daughter cut ties with him, seeks a change of name.

Elon Musk's transgender daughter Xavier Alexander Musk has applied to legally change her name and gender, saying she no longer wants to "be related to my biological father in any way, shape or form".

The 18-year-old has asked to be recognised as female and have the name Vivian Jenna Wilson.

The petition for both a name change and a new birth certificate was filed with the Los Angeles County Superior Court in Santa Monica.

There was no further detail of the apparent rift between Mr Musk's daughter and her father.

The Tesla and SpaceX entrepreneur has yet to comment.

Mr Musk was married to Vivian's mother, Canadian author Justine Wilson, from 2000 until they divorced in 2008.

Their first son, Nevada, was born in 2002, and died of Sudden Infant Death Syndrome (SIDS) at 10 weeks.

Mr. Musk's  children have kept a relatively low profile despite their father's fame.

On Father's Day, the entrepreneur tweeted that he loves all his children.