How to calculate the value for each month, provided that the data is collected for 90 days?

Question

PostgreSQL

There is a table: date_name, name

The need is as follows:
Output count(name) by month, but the condition is that name is considered in the interval from "end of the month" to "end of the month - 90 days"

Example:
September - count(name) where date_name between date' 07/02/2020' and date'09/30/2020'
and so on for all months.
those. As I understand it, this is a nested query, but I still don’t understand how to organize it.