My new H1b with X company and what to transfer to Y company(Currently working).
but my Y company reducing Designation and Salary. is it allowed?
is there anyway to keep same Designation as per my current LCA?
As far as the salary is at or above the minimum wages prescribed for the SOC , which is a requirement for the LCA to be approved, your employer is good. Designation may drive the wage level and that is something you need to discuss with your employer.