WARNING: This is an approach, not necessarily a complete solution. Your Odoo Digital Advisor or Odoo Partner can help you if you don't have the skills to do this yourself.

One option is to create an Automation Rule that overrides the function that Odoo uses to add the period description with the start and end date. This function relies on the recurring_invoice field on the subscription order line.

This approach creates a new sale order line with the same name and since we are not providing a value for the recurring_invoice field, we can recalculate the description on the copy and assign the result (which won't have the period text) back to the original.

for record in records:
    if record.sale_line_ids:
        sol = record.sale_line_ids[0]
        sol_duplicate = sol.new({'order_id': sol.order_id.id,'name': sol.name})._prepare_invoice_line()
        record['name'] = sol_duplicate.get('name', record.name)