There can be no doubt that 'Abu Ba'ajah' is the true name of the Muslim Prophet.
The historical evidence for it is very good.
It's imperative in this regard, however, to clarify the use of the 'Abu-Naming' System of persons in the Arabic language. In formal Arabic, the words (Abu, Aba, & Abi) mean 'father, dad, daddy, pa, & papa'.
Historically, there are four types of this naming system:
[1] The Classical 'Abu-Naming' System:
http://ccat.sas.upenn.edu/~bvon/images/map1.gif
In the pre-Islamic period, the word 'Abu' is always used as a prefix for forming proper nouns. For example, the name of the first Caliph is 'Abu Bakr':
http://en.wikipedia.org/wiki/Abu_Bakr
This is a real name. In other words, this Caliph had no son called 'Bakr'. 'Abu Bakr' was just a name given to him on his first birthday. The same applies to the Muslim Prophet. He had no daughter called 'Ba'ajah'. 'Abu Ba'ajah' was just a name given to him on his first birthday as well.
[2] The Asian 'Abu-Naming' System:
http://www.yale.edu/ceo/Projects/swap.html
In the Arabic speaking countries east of the Suez Canal, i.e. (the Gulf States, Yemen, Iraq, Lebanon, Syria, Jordan, Gaza, and the West Bank), the 'Abu-Naming' System is used today to generate nicknames of persons in a pre-defined manner. Suppose for instance that someone is called 'Abraham'. As soon as this 'Abraham' comes of age, his friends start calling him 'Abu Isaac' and 'Abu Ishmael'. Why is that? It's because, according to the Bible, the old Abraham had two sons called 'Isaac & Ishmael' respectively.
[3] The Egyptian-Sudanese 'Abu-Naming' System:
http://www.atlapedia.com/online/maps/political/Nth_Africa_E.htm
In Egypt and Sudan, the 'Abu-Naming' System is used arbitrarily to refer to an actual father by the name of his first-born son or daughter whatever that name happened to be. And mainly wives in referring to their husbands use the 'Abu-Naming' System.
[4] The North-African 'Abu-Naming' System:
http://www.mytravelguide.com/travel-tools/maps/North-Africa-map.php
In the North-African countries, i.e. (Tunisia, Libya, Algeria, Morocco, the Western Sahara, & Mauritania), the 'Abu-Naming' System is used differently. Here, the word 'Abu' means 'son of ' instead of 'father of'. Accordingly, the 'Abu-Naming' System is used, in these countries, to refer to sons by the names of their fathers.
These differences in the use of the 'Abu-Naming' System must be taken into account in any historical research to pin point the actual name of the Muslim Messiah.
The Muslim Prophet got the name 'Abu Ba'ajah' in the Classical Period. And hence, when ancient poets called him 'Abu Ba'ajah', those poets were referring to a real name and not just a nickname of the contemporary types.
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Dear Muslims;
You have to realize that your Prophet couldn't be the 'Messenger of Allah', because first and foremost there is absolutely no 'Allah' anywhere inside or outside the vast Universe:
http://www.sciforums.com/showthread.php?t=22326