If you are the client, you can sign an agreement with the design company, which stipulates that the patent belongs to you.
Otherwise, if there is no agreement, according to the provisions of the patent law, the patent belongs to the inventor, that is, the design company.
Article 8 of the Patent Law stipulates: For inventions and creations completed by cooperation between two or more units or individuals, or for inventions and creations completed by one unit or individual under the entrustment of another unit or individual, unless otherwise agreed upon, the application shall The right to a patent belongs to the unit or individual who completed or co-completed it.