1. Arabs are very proud of their families/tribes and won't exchange that for the world - husband or not! Some do take Madame or Mrs so-and-so ... just in a few social circles, like dinner and Embassy receptions, etc, where invites go to Mr and Mrs bla bla, in keeping with Western traditions. However, an official change of name would involve going through legal channels and court and isn't something I have heard anyone do.
2. In Arab and Muslim societies, though the perception is that women are 'owned' and 'controlled', a woman is considered as an independent human being, with her own name and her own property and wealth. In Islam, a woman has always kept her own wealth, property and inheritance. If she is employed, she keeps her own earnings. At the same time, Islam commands her guardian (father or brother or uncle, if she isn't married and husband, if she is) to provide for her and keep her according to her status and position. It is basically a case of what is hers is hers and what is his, is hers too! This means that a woman has no financial obligations - but is entitled to rights. If a woman is working, sharing her income with her family or on her household, is totally up to her. This is the case in theoretical Islam, where women on paper have more rights than the most progressive ideologies any where and at any time, considering that those laws were 'enacted' around 1,500 years ago. Reality, of course, is another thing, as Muslim men continued to uphold pagan traditions and allowed their insecurities to get the best of them, when it came to women's rights.
3. Every name has a meaning in Arabic and perhaps a story behind it. The Al before many names means 'belongs to the family/clan of.' Family names are passed down from one generation to the other, along with family trees, and oral as well as written history. Arabs have always maintained their lineages, with a lot of families able to trace their roots down at least 10 - 40 grandfathers. Last names either connote a profession (like the carpenter, the jeweller, the teacher, the clergyman, etc), a geographical area (the arab, the persian, the bahraini, the kuwaiti, nabulsi, hindi, humsi, masri, etc), a trait of an ancestor (the brave, the kind, the drunk, etc) or the name of an ancestor, who is known in history. Arabs would be able to recognise where other Arabs come from, along with their sects, religion and country, by closely examining their names.
A colleague of mine at Global Voices Online has asked our global team of bloggers about the tradition of changing names after marriage in their countries. I have written a few points, but if you can think of some more, please feel free to chime in: