Is it permissible to collect donations to purchase incubators from the merchant who is a partner of the questioner and donate them to those in need at a price that pleases Allah, while concealing the fact that the incubators belong to the questioner?

You are not permitted to buy from yourself in your capacity as an agent for the donors, unless they explicitly authorize you to do so. This is because an agent is a trustee, and it is not permissible for him to combine two purposes in a contract. However, if the principal gives permission, then he is allowed to buy.