In some instances, yes. If you currently own anonymous donor sperm or eggs, you can transfer ownership of the materials to a specific person. Both parties (current owner and new owner) will need to complete paperwork that is either notarized or signed in front of a Family Fertility CryoBank/Fertility Center of California employee. Please note that there is a fee for time spent on coordinating this transfer.
If you would like to transfer ownership to another person but you did not complete the FDA CFR Title 21 Directed donor testing at the time of creating the materials, then these materials cannot be used by anyone other than yourself.
It is important to note that most IVF facilities require a legal agreement to be constructed by a lawyer to transfer ownership of reproductive tissues.