Ok, maybe it's dumb in Obi-Wan because it's dumb in Star Wars III - Revenge of the Sith, BUT ....

You have a HUGE secret to keep, from the most powerful (or maybe the second most powerful) man in the whole Galaxy. What do you do?

You take one kid, give her a new name, a new family, on a totally new world ... not bad. That is a secret that MIGHT be kept.

You take the other kid, KEEP the name Skywalker, TAKE him the powerful guys home world, LEAVE him with the Uncle (all still using the Skywalker name), and you hang out keeping your last name as well. WHAT kind of secret keeping is that?

It's kind of like .... not really keeping a secret at all. You are pretty much advertising it to everyone.