The charity was established in 1854 and is best known for its Bethlehem carol sheet, used in thousands of churches across the UK.
As part of the re-brand, the charity has changed its logo to incorporate open hands and a cross.
Chief executive Jeremy Moodey explained the motive behind the change: "We want to challenge Christians in the UK to look at the Middle East through new eyes, to see the many needs in the region but also the diversity of local Christian responses, whether it is in healthcare, special needs education, work for refugees or community development.
"Our new name describes exactly what we do – embracing the people of the Middle East with Christian love and compassion."
The name change has the support of Bishop Angaelos, leader of the Coptic Orthodox Church in the UK, who has become a patron of the charity.
Embrace the Middle East also announced its five-year campaign to raise £20 million to change the lives of vulnerable and disadvantaged people in the region.
As part of the re-launch, the carol sheets will be now be distributed as a church resource free of charge.
"Giving our famous Bethlehem Carol Sheets away is just one part of this campaign. We would rather use the carol sheets to highlight our work, and that of our Christian partners in the Middle East, than make a modest profit through sales," said Moodey.
"We are also excited that His Grace Bishop Angaelos has kindly agreed to become a Patron. Embrace is increasing its support of projects in Egypt, given the many needs there, and we have already established a good relationship with the Coptic Church in the UK.
"We are thrilled at this opportunity to strengthen further our links with Egyptian Christians in Britain."