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The problem you are solving is most commonly called “fuzzy string matching”. There are a bunch of algorithms for it (some of which are described in this thread) depending on your specific requirements. I’d start with an existing fuzzy string matching library (e.g. thefuzz, for python) and calculate matches between your input letter cases and your list of names. This sounds pretty reasonable to do fast since fuzzy string matching is commonly used in text editors to make it easier to find files. If you start with a fuzzy string matching library, I wouldn’t worry about asymptomatic complexity until you actually see a performance problem.