In English there was analysis by John Wells defining several lexical sets for vowels [1]. Various other linguists have extended that to cover other accents such as Scottish, Irish, and Welsh.
Words in the same lexical sets are the result of splits and mergers. Usually through processes like you describe -- e.g. the Southern English BATH vowel resulted from a lengthening of the TRAP vowel and then changing quality to that of the PALM vowel.
Lexical sets don't cover consonant changes between accents such as rhotic r, the /sh/-/sj/ merger in shore and sure, tapped t, glottalized t, etc.
And on the thing you are talking about, Colin Gorrie has some YouTube videos on doing that comparative linguistics and rule construction. A lot of his videos are doing that for conlangs, but there are videos with real historical accents in several languages.
An example in English is the shift in pronunciation of 's' before 'u' from the /sj/ glide to the /sh/ sibilant so that in accents with that shift <sure> and <shore> are homophones (especially with the CURE-FORCE merger).
There are computer programs that you can use to express these rules and see how the pronunciations change over time. I think Colin uses one in some of his videos and Biblidarion uses one in some of his conlang videos to check phonetic evolution of his conlangs.
I forgot to mention that we struggled much more with cognate names that that were more linguistically distant than within ones that were closer. e.g. Matthew, Mattieu were likely to be within the same lexical set, but Matityahu may have been a bit to far for us.
It's interesting how some names tend to have more conserved features than others as they transit across larger distances in terms of language families. I worked later in genetics and was able to reapply many of the learning from names into gene sequences.
I used to test our own software with my given name. It's rather common, but our ruleset would produce some rather wild variations of it. We thought it was an error, but it turned out to be a completely valid name in Finnish!
Words in the same lexical sets are the result of splits and mergers. Usually through processes like you describe -- e.g. the Southern English BATH vowel resulted from a lengthening of the TRAP vowel and then changing quality to that of the PALM vowel.
Lexical sets don't cover consonant changes between accents such as rhotic r, the /sh/-/sj/ merger in shore and sure, tapped t, glottalized t, etc.
And on the thing you are talking about, Colin Gorrie has some YouTube videos on doing that comparative linguistics and rule construction. A lot of his videos are doing that for conlangs, but there are videos with real historical accents in several languages.
An example in English is the shift in pronunciation of 's' before 'u' from the /sj/ glide to the /sh/ sibilant so that in accents with that shift <sure> and <shore> are homophones (especially with the CURE-FORCE merger).
There are computer programs that you can use to express these rules and see how the pronunciations change over time. I think Colin uses one in some of his videos and Biblidarion uses one in some of his conlang videos to check phonetic evolution of his conlangs.
[1] https://en.wikipedia.org/wiki/Lexical_set