Don't most people who owe other people money pretend not to know their debtors?

Anyways, you have two options.

1) Have the doppelganger act out of the ordinary, and be prepared for characters to spot it (or not). In particular with PBP gaming, unless you point out that someone is acting uncharacteristically, most players won't get it. But if you do choose this option, consider what to do if they figure it out. What is the evil overlord's backup plan? The prudent world conqueror always has one. Perhaps the dopplegangers control the courts and direct witch hunts away from themselves, employing the PCs.

2) Have the doppelganger not act out of the ordinary. Maybe he spent a few months observing the noble as a servant in his house, maybe he reads minds - the point is, the players are unlikely to call you on 'why did we not notice that this consummate master shapeshifter was not the person he appeared to be?' The answer being, he's a freakin' doppleganger, b**#*! . He does what he wants!

If the plot requires that the players not be able to guess right now, don't give them the chance. It's as simple as that.