Someone who has an Arabic name is usually an Arab or Arabic in descent. They usually speak the language Arabic and predominantly live in North Africa or the Middle East. They are a Semitic people, like the Hebrew-speaking Jews.
An Arab is not necessarily a Muslim and a Muslim is not necessarily an Arab. Islam was founded in an Arab nation and the Qur'an is written in Arabic. However, Islam spread to many other parts of the Old World immediately following its founding, to places where Arabs do not reside, such as Indonesia, which is the largest Muslim state. Therefore, there are many more non-Arab Muslims in the world than Arab Muslims. Arabs however are also Catholics and there are even some Arab Jews.
He is an Arab who lives in Saudi Arabia.
Abdullah is an Arab, but he does not practise Islam.
Also, to point out something else. In the twentieth century, Arab nationalists have been trying to form a pan-Arab state, ever since the Ottoman Empire ended in the Arabic-speaking lands. These have been in the form of countries like Egypt (Nasser), Syria and Iraq (Saddam Hussein), with the Ba'athist party. These people should not be mistaken for Islamic fundamentalists, as they are usually secular and Marxist, and are not Muslim in any way. Fatah in Palestine is an Arab Nationalist group, not Islamic.
The British Isles are an archipelago of islands off North-Western Europe. The two largest islands are Great Britain and Ireland. Great Britain consists of three countries: England, Wales and Scotland. Ireland consists of two countries: Northern ireland and the Republic of Ireland. Great Britain together with Northern Ireland make up the United Kingdom of Great Britain and Northern Ireland (UK).
Many people mistake England for an island, which is because of the extensive use of English as a vernacular across the island of Great Britain (although Welsh and Gaelic are also used a lot). England is just one of the countries of Great Britain, if one is to call it a country, as it does not have its own government (unlike Scotland and Wales). Britain and England are not interchangeable, despite England having the UK capital.
The British Isles has five different countries.
England is not one of the islands of the British Isles!