The name change is part of a campaign to support the England team and the company's official charity Centrepoint.
The agency is bidding to be the UK's most football-friendly workplace over the next month. It will be using the tournament to raise more than £3,000 to fund 25 rooms at Centrepoint services for the young homeless for the next year.
The agency will also change its logo to a new England-inspired design, redesign its website and include new email addresses for all of its 130 employees.
All games will be screened live in the agency's bar and Centrepoint will receive £100 for every goal England score in the group stage, with £150 per goal donated for every knock-out phase game.
In addition, all goals scored by any team from outside the penalty area in the group stage will be worth £50 to the charity.
WAGs will also play their part, with Centrepoint gaining £25 for every Wag featured on a national newspaper front page, which will be doubled for those wearing over-sized sunglasses.
In addition, employees who don an England strip for games will raise £10 each for the charity and everyone will get a McDonald's breakfast on working mornings after England games.
Red and White chief executive Mike Morgan said: ‘We want to be the UK's most football-friendly workplace and help the young homeless. It's good business for our people to be able to enjoy the tournament and know they're supporting a very good cause as well.'