Quick, name a famous obstetrician. [Cue Jeopardy theme music here.]
Now Google “famous obstetrician.”
Forget it, we'll just tell you the answer: none. There are no famous obstetricians. Yours may be the first face a baby sees, but that's a fleeting fame. You won't be dodging paparazzi. More like pooperazzi, which is very, very different.
The power of your position will likely be counterbalanced by your anonymity. If you do find yourself in the limelight, pray that it isn't because of your involvement with crazy people (cough, cough--Octomom--cough).
Will you step (or be pushed) into the spotlight for your decision to perform abortions (or not)? Some obstetricians have been killed for their choice. It's a slim chance, but not the way you'd like to end up in the news.
You could also pursue fame as an author or an advocate. Good books about healthy pregnancies and motherhood are always best sellers. More than half of all babies are born to single women. Radical social changes like this bring huge opportunities for growth and change. You can become an expert on breastfeeding options for gay men raising an infant, or become the official Oprah expert on multiple births, or postpartum depression.
You might become famous as the doctor who helps infertile couples, but don't get too good. Insurance companies don't cover fertility treatments very easily. Doctors who don't play by the rules or are considered unscrupulous make good headlines.
Also, in case they don't teach this in med school anymore: don't impregnate your infertile patients with your own tadpoles. You'll get jail time and the fines will definitely shrink those bulging pockets. The Sperminator. Oh yeah… and a cure for breast cancer could get you on a few talk shows.