how free really are people in forming an identity
maybe a good direction to take this question is first identifying what it is exactly that freedom consists in. In the Anglo-American context, ‘liberty’ is commonsensically taken as the absence of interference or resistance on the part of external agents (which always break down into two types: 1. other citizens 2. the state), what’s commonly called negative liberty.* Given this and given that the site of identity formation is going to be a political one, so through political institutions, I guess I’d say that, in America, people are as free to form identities only to the extent that they can associate, assemble, enfranchise themselves, etc., without experiencing resistance or interference.** But I’m not sure how much of an answer that is.
and who gets to define the good life in the first place?
id tentatively say it’s hammered out in the same process as other political contestations are, so negotiated in public discussion, as well as just lived out or enacted by the way people live their everyday lives. I’ve seen critiques of contemporary liberalism (big tent liberalism, not Democratic Party liberalism) that maintain its this exact question, along with the actual definition of the good life, that’s crucially missing in political discourse today, as it’s been supplanted by technocratic language of which means to employ to reach the most Pareto efficient outcome.
*this is not the only definition of liberty
**there are ways of being and doing that are obviously political but aren’t constitutionally enshrined, so add to this list the freedom to produce, labor, migrate, etc.