You are doing research in the 1600s. The family name you are looking for is Fleming with one M. You know that there is another family group called Flemming, with two Ms, but your family has always prided itself on using one M, according to Grandmother Mary. You know that the family was at a specific farm at a specific time - but there are no entries for your Flemings in the Parish Registers. Idly flipping through the registers, you see the whole family called Phlemmynge. What does this mean?
Surnames are a relatively recent invention. Many centuries ago, the population was fairly sparse., mostly poor, and did not move around much. The usual way of identifying a person was by his trade or place of living. So we have John the Miller, and Widow Mary at Barton Farm. Who needed a surname? After all, anyone who needed to know you, already knew who you were. For example, how many surnames appear in the Bible, with its cast of thousands of characters?
About a thousand years ago most of Western Europe had been overrun by North Germanic tribes, which tended to use patronymics. King Harold of England was Harold Godwinsson, because his father was called Godwin. Over the next two or three centuries, with the improvements in public order (fewer wars), surnames began to develop among the aristocracy, particularly since the right to inherit depended on the connection with ancestors. The De Lacy family, which owned substantial land in northern England, was named after their place of origin in France. After 1066, they started using this description as a surname. Yet two centuries later, the last non-royal Earl of Chester was John le Scot, John the Scotsman had no surname at all.
But populations grew, and then shrank because of disease. People started to move around. Economic wealth increased, and caused people to congregate in towns and cities, where there might be dozens of people called Roger who were bakers. Governments were becoming expert at collecting taxes, and to do this you need to know who your citizens are. So in 1379 in England, when a poll tax was levied, a list of everyone over 16 was required. There had to be some means of distinguishing one William from another. Again in 1413, a law was passed requiring that every legal document contain the full name, occupation, and place of abode of every person who signed. These gradually caused everyone to settle on a fixed surname, and by 1500 most people had done so.
Most surnames are based on occupations (Bowman, Smith etc.); or locations (Hill, Rivers, etc.); or place names (Worthington, Middleton, etc.); or physical or personal descriptions (Whitehead, Strange, etc.). Some of the originals have undergone weird and wonderful transformations, for example atten Ash (by the Ash Tree) became Nash.
Saying a surname and writing it are two different things. Early records were kept in Latin, so that Henry Bridge might be recorded as Henricus Pontis. As more records were kept by less educated people, such as parish clerks, spellings depended on what the owner of the name said, and how well the clerk could spell. But now they were written in English.
Let’s assume a person was called Harding. He tells the clerk his name, and it is written as said Arden. Or perhaps there is another family in the area with a similar name that the clerk knows, so he writes Hardinge. Frankly, until about 150 years ago, almost any spelling that sounds like the name can be found. My own six-letter surname has 270 possible variations, ranging from Fitun through ffettune to Phytan. I’ve found three different spellings of, the same name in a one page Will.
So my response to a person, who is researching Fleming and finds Phlemmynge at the right place and time, is congratulations on finding another of the pieces to your family jigsaw puzzle. And of course for the future, collect all spellings of all variations of your family name.