“Dr Fischer, is it okay to apply to two programs in the same hospital?”
First of all, there is NOTHING unethical or unprofessional about doing this. Second, there is virtually no chance of anyone knowing.
Try not to interview with both places on the same day:)
For example, you do not have to go in disguise, removing glasses or a new hat to hide yourself.
Also, it is like looking for a new husband. Is it okay to see two men living in the same building? YES!
Should you tell them “By the way, I like this building I just went on a date with your next door neighbor last night!”
NO! Just like dating, don’t tell people about the competition. that is different.
Again it is NOT unethical or illegal to apply to two programs in the same hospital.