[wobbly_bush]

> Why don't people just change their names to the caste they want to be

For an over-simplified explanation, substitute caste with race/nationality and rephrase the question in a setting you might be more familiar with. For example "if people face racism/discrimination due to their nationality, why don't they just do X", where X is to obfuscate their race/nationality. It might work sometime, it might not work most of the times and the real answer is complicated and depends on the details. If you consider everyone in India to be culturally homogeneous, then it's just a matter of saying someone isn't caste X but Y. But if you consider every caste/subcaste to be distinct culturally and linguistically (almost like they are their own countries), it's not trivial to replace surname X with Y as other factors give you away.

> Is there a reason that such a backwards obviously oppressive system persists to this day in 2023?

Similar mental analogy helps understand a tad bit better - why do oppressive practices like racism/discrimination based on nationality exist today? At that, exist in some of the more developed countries. FYI - caste based discrimination is illegal in India, kinda similar to how racism is illegal but that alone isn't sufficient to remove it from the culture.