If you want to read two families books about this, I recommend Misconception, written by Shannon and Paul Morrell. Their embryo was implanted into the uterus of Carolyn Savage, who is also writing a book about her experience of carrying another woman's baby, which will be titled Nine Months to Give. This particular mix-up, like most, happened because of the way the embryos were labeled. Shannon's maiden name was also Savage, and the embryos were were labeled as such. That is how one woman's last shot at pregnancy (for medical reasons) turned out very different to what she had intended. She became an unintended surrogate mother, who was advised to carry out an abortion, but refused. What conclusions can you make from stories like these?
First and foremost, I think, that it is crucial to ask your fertility clinic lots of questions about steps they undertake to stop mix-ups from happening. Do they store embryos listing your full name? Do they triple check that the embryos implanted into your uterus are yours, and various stages of the process? Do they have other patients with the same family name? What measures are in place to take additional care that families with the same names do not experience mix-ups? Have they ever had a mix-up? These questions are, I believe, crucial ones to ask. Add them to your "how to choose a fertility clinic" check list. Embryo mix-ups are real, and you want to minimize the chances of one happening to you.