I don't think the generation names are 'internet jargon' as they are used in Psychology and behavior management and, I have a feeling, in marketing too.
This is an example of names that are used.
The Lost Generation/The Generation of 1914: 1890-1915
The Interbellum Generation: 1901-1913
The Greatest Generation: 1910-1924
The Silent Generation: 1925-1945
Baby Boomer Generation: 1946-1964
Generation X (Baby Bust): 1965-1979
Xennials - 1975-1985
Generation Y/The Millennials/Gen Next: 1980-1994
iGen/Gen Z: 1995-2012
Gen Alpha: 2013-2025
Depending on who you reference the names can be different but the date remain very much the same as they are influenced major cultural, political, and economic events.
Although some do refer to those born either side of 2000 as "the snowflake generation" it is unhelpful and pejorative. The idea of understanding 'a generation' is about understanding the greatest influences on their younger years and therefore giving us understanding about how they will behave in a given set of circumstances.