Beyonce and Jay-Z have named their twins Rumi and Sir Carter.

The couple - who already have five-year-old daughter Blue Ivy together - welcomed the latest additions to their family earlier this month and have now filed trademark documents for the names with the United States Patent and Trademark Office, TMZ reports.

The website added that the trademarks are for ''fragrances, cosmetics, key chains, baby teething rings, strollers, mugs, water bottles, hair ribbons, playing cards, tote bags, sports balls, rattles and novelty items''.

Meanwhile, it was recently revealed that although the pair are ''totally exhausted'' after welcoming their twins, Beyonce, 35, and Jay-Z, 47 - whose real name is Shawn Carter - have never been happier.

A source said: ''At nights, Beyonce has been overwhelmed with all the work needed caring for two babies. Despite all the help they are receiving, Jay is still pitching it so that Beyonce has total support.

''Neither Beyonce, nor Jay, have been able to enjoy an entire night of sleep since the twins arrived. They are totally exhausted but at the same time have never been happier as a family.

''Jay-Z is on super dad duty as he has been completely hands-on with the new babies, helping with late-night feedings, burping, and also changing diapers.

''But Jay hasn't stopped there, he has also been spending a ton of time with Blue during the day and their relationship has grown since the new babies arrived.

''Jay watched Beyonce do heavy all the heavy lifting when Blue was born so he is doing his best to be more present with the twins.''

In contrast to their baby joy, the couple are said to have become frustrated in their attempts to find a new family home in Los Angeles.

The duo recently returned to their $400,000-a-month Malibu estate with their baby twins, but their lease of the property ends this summer and they are yet to seal the deal on a new abode.

A source explained: ''They want a super baller, crazy estate, and the ones they love are going for $150 mil.''