From my understanding, there is not much difference in terms of the Greek letters or Latin letters to represent the 'true' value of parameters in OLS. If you're referring to the estimates of these parameters, $\hat{\beta}$ is used more frequently than $b$.

In general, Greek letters are more often used as it's convenient to treat $\alpha$ as $\beta_0$ so that the expression can be written as $Y = \beta^T X$ in multivariate regression. In the world of machine learning, the expression is often written as $Y = w^T X$.