A seed note. Replace or delete it.
Two records land on your desk. One says Fatima Abdullahi. The other says Fatuma Abdulahi. Same person, or two people?
You cannot look it up. There is no row in a table that answers this. There is only evidence, and evidence is incomplete, noisy, and sometimes contradictory.
That is the whole problem. Everything else is detail.
What the maths actually gives you
The standard method is nearly sixty years old. Fellegi and Sunter wrote it down in 1969, and it still sits underneath most of the tools people use today.
For every field you compare, you ask two questions. If these two records really are the same person, how often would this field agree? And if they are different people, how often would it agree anyway?
The ratio between those two numbers is the weight of the evidence. Agreement on a rare surname is strong. Agreement on a common one is nearly worthless. Add the weights up and you get a score.
Here is the part people miss. That score is not a fact. It is a belief, and it is only as good as the assumptions you fed it.
Why it goes wrong on names like mine
Two failure modes, and they pull in opposite directions.
One name, many spellings. Diallo and Jallow are one Fula family name split by a colonial border. A string matcher sees two words with almost nothing in common and says different. It is not calculating wrong. The fact it needed was never in the records.
Many people, one name. Two records both reading Ibrahim Musa, both in Kano. Everything agrees perfectly. They are still probably two different people, because in a city of millions that name is not evidence of anything.
Turn the threshold up and you fix the second problem while making the first worse. Turn it down and you get the reverse. You cannot fix both with one dial.
That is why the answer is data, not a better algorithm.
There are two paradoxes sitting underneath all of this, and it helps to know they have names. Where “similar” becomes “same” is the sorites paradox, and whether a thing survives being changed is the ship of Theseus.