You can do that by inheriting mail.wizard.invite TransientModel and then add onchange method for partner_ids fields, loop the  partner_ids and then get the names of the partners and add them to the message field.

The below is working if you invite only one follower but if you want o add all partners you need to get the message as xml and then replace the first p tag:

from odoo import api, fields, models, _

class Invite(models.TransientModel):
    _inherit = 'mail.wizard.invite'

    @api.onchange('partner_ids')
    def _changepartner(self):
        msg = "Hello "
        if self.partner_ids:
            for partner in self.partner_ids:
                msg = msg + partner.name + ","
            self.message = self.message.replace("Hello,", msg)