Not... really?
I mean, there are some limitations but off the top of my head.
Automated record keeping already tracks ships and their demonstrated traits. This could be an issue.
Setting a transponder to a false identity if there's no sensor in range to detect the ship has the AI handle it as if the ship is the false identity, this includes diplomatic impacts. Even if the ship is acting in ways the class strictly speaking should not be capable of, the AI discards the discrepancy and does not update the false identity (to prevent a jumble of contradicting data screwing things up).
If there is a sensor in range, the AI may register something is strange if the demonstrated thermal signal is higher than what the database says it should be capable of (as engine power and thermal signature can be dialed down), or if the EM signal is different from what it should be (shields and sensors both project known amounts of EM signal).
If the AI register's something is strange it may send a ship to investigate with active sensors. More course resolution active sensors are less effective/slower at the edge of their range than finer resolution sensors at correcting a false identification, and grow more effective more slowly than finer resolution sensors (ie, a 50 HS resolution sensor can start with identifying at greater range than a 5 HS resolution sensor, but that 5 HS sensor will have much better chances at any comparative range).
In case of salvage, if an empire knows who was supposedly in combat and can salvage the wrecks, there's a chance that the empire figures out that the damage done does not fit the damage profiles of what weapons it has on record that are appropriate to the combatants. It will record this separately as the correct part with a confidence value. More hits on the same salvaged ship make the confidence value higher. If it's allied with the owner of the destroyed ship it may pass this information along.
In case of salvage, if it identified that the damage profile is incorrect it will check its database to see if it knows the correct component and any similar components. If it does, it rolls and checks the result against how confident it is it properly identified the component. Even if the roll doesn't result in accurate identification of the component, if it has records of similar components from the same empire it is more likely to accurately identify the empire responsible.
If an empire accurately identifies which empire is actually responsible for the damage it is likely to share this information to its allies, and may share this information with a hostile empire they are not at war with but were the victim of the attack. It may share this information with neutrals, and will not share this information with enemies.
So long as the false identity holds up any action taken by the ship with the wrongly set transponder will be pointed to whatever empire is being framed.
If the false identity fails the perpetrating empire sees a diplomatic hit with the empire it was fooling. If the empire that was being framed finds out the empire that was framing them also takes a diplomatic hit with the framed empire. This hit is smaller if both the framed and framing empires were allies and hostile or at war with the empire that was being fooled.
Faking the identity of a civilian ship as another civilian ship or a military ship with another military ship that is of your own empire gives a smaller diplomatic hit. Faking the identity of a civilian ship by a warship gives a bigger diplomatic hit.