Middle names may be added, but that is not all that may occur. Entire given names may become re-arranged as in the case of my Great Grandfather, born Dietrich Wilhelm Buhr (I have the birth record from the local Lutheran Church with his mother and father noted), but afterward referred to as William D. Buhr. There are a few points to consider. No other William Buhr or Wilhelm Buhr or Dietrich Buhr is found in the county or surrounding counties in the time frame of his birth, nor after his birth, nor when he was married. The tradition of his family, who emigrated from Grand Duchy Oldenburg (located now in Niedersachsen, Germany), was that the middle name was often the most used given name. This tradition is reflected in his grand father's and father's names and mostly in the names of his siblings. He was the first child of his family born in the United States following immigration sometime in late 1842 or early 1843. Yet, rather than being called Wilhelm or Dietrich, all other records refer to him as William D. Buhr including his father's probate records, his guardianship records (he was orphaned) his Civil War service record, all US census records where he appears, and in the Civil War pension records for his surviving minor children. Based on this evidence and more, I conclude that his birth name was Dietrich Wilhelm Buhr, but he was called by the Americanized name, William D. Buhr. Given names can be changed drastically sometimes and still be the same names in a different tradition or context. Just sayin'.The commentator makes an important point, often overlooked by genealogical researchers. I can remember many instances over the years when helping patrons at the Mesa FamilySearch Library, that potential ancestors were rejected because the name in the record differed from the one "accepted" by the researcher. The spelling of a name or even the arrangement of the given names is not a crucial issue in identifying an ancestor or other relative. Names can be changed at a whim. For example, when I was young, my family consistently called me by a nickname. As I got older, I insisted on being called by my full given name, but until I got as old as I am now, there were still friends of my parents who knew me only by my nickname.
The rule for genealogists is that a person is recorded by the name given at birth. Later name alterations or changes are reflected in notes or alternate name designations. Notwithstanding that rule, there are exceptions. Another example is the name of one of my Great-great-grandfathers. His birth name was Charles Godfrey DeFriez. Later in life, he legally changed his name to Jarvis, his wife's maiden name. From the time of his marriage, he also used the surname Jarvis. As recently as today on FamilySearch.org's Family Tree, I find that his descendants list him as a child of his wife's parents making it appear that he married his sister. It would have been very strange indeed if his wife's parents had "adopted" their son-in-law. What is even stranger is that I have corrected this error in Family Tree a number of times. Those who make the change showing him as a child in his wife's parents family seemingly ignore the social and cultural consequences of their insistence on including him in the family.
Again, referring to the comment above, you should note the importance of accurately and exhaustively researching the place where events occurred. The commentator gives us an excellent example of this when he notes that a search has been made in a variety of records to confirm the conclusions regarding the changes in the ancestor's name. It is apparent that the people changing my own ancestor's family origin are not so diligent.
One common myth that I hear continually concerns the changing of a name at the time of entry of an immigrant into the United States. It is abundantly clear from history, that many immigrants Americanized their names at the time of immigration, but this practice was far from uniform. The myth is that this was done by the United States government at the port of entry as a common practice, which was not the case. What is even more interesting is that many of the immigrants had already adopted a different name in their country of origin. My wife has found this with her Swedish ancestors and I have found this with at least one of my Danish ancestors. Those name changes came about as a result of the governments requiring their citizens to adopt a permanent surname instead of using the name changing patronymics. In the case of my wife's ancestor, his name was changed when he was in the army in Sweden, long before he came to America.
Another very common issue among unsophisticated genealogists is the "same name-same person" issue. This involves combining families where the parents have the same names into one family simply on the basis of the name. The list of errors engendered by sloppy research and unwarranted assumptions about names could go on and on. Caution is advised and also more extensive research.