Is it permissible to purchase a commodity or have work done in the third person, with the intention of buying or having the work done for myself, without the seller or service provider knowing that I am the other party, for fear of envy or greed?

There is no objection to purchasing for yourself or accepting work without informing the seller or employer that you are buying or working for yourself, unless there is fraud or deception involved. Selling and leasing are valid by mutual consent. Allah Almighty says: "O you who have believed, do not consume one another's wealth unjustly but only [in lawful] business by mutual consent." And the Prophet, peace and blessings be upon him, said: "Indeed, selling is by mutual consent." The buyer is not obliged to inform the seller of his identity, and concealing the buyer's true nature is not objectionable, especially if it is for a valid purpose, while avoiding lies and instead using allusions and كنايات (euphemisms/indirect expressions).