@jmahmoud, I am no expert so I cannot give you any legal advice. Are you willing to share what the other country is? All I can say is that, if I were you, I would complain, and I would specifically ask why they entered those details, since every other dual national does not seem to have that. The complaint might have a bit more strength if you can elaborate on some specific inconveniences, eg you visit a country which does not have good relationships with your other country, and even just showing that note in a hotel is something you might want to avoid, eg you might not want to brag about an Israeli passport in Saudi Arabia or viceversa.
@DoctorAllcome, a lot of what you have said is nonsense.
You seem to not appreciate that you can be a citizen of a country even if you don't hold a passport. Your confusion may derive from the totally idiotic British system, in which in theory a passport isn't compulsory, but in practice it is (see Windrush). In many other countries, citizenship gets recorded at birth, or on other, often compulsory and cheaper, documents, like an identity card (you do realise that a country with compulsory id cards CANNOT have something like the Windrush scandal in which citizens are illegally deported, right?)
Eg if a dual British German citizen gets arrested in Germany, the UK won't be able to provide consular assistance. Whether this person ever had a German passport and whether this was in any way recorded by the British authorities is utterly, completely and totally irrelevant. There are many ways the German authorities could know that person is German: birth records, identity card, other records, etc. Can you please explain what is the relevance of, and what changes if, the Home Office knows of the German passport?
As for ghosting the chips, I have no idea what you are talking about. Not saying you are wrong - just saying I am clueless. Can you please elaborate?
A dual national with a current passport is asked to provide more proof of identity. Why on Earth a dual British German citizen should provide his German passport is beyond me, nor have you explained it. If I have degrees in both law and medicine, I don't need to prove my medicine one to practice law, and viceversa!!! What sort of a convoluted reasoning is yours?
I am of course not advocating deliberately 'losing' a foreign passport. Just saying the rule is stupid because it inconveniences those who have nothing to hide, while those who do can circumvent it all too easily. Clearer now?
In fact, since passports last 10 years, one could time the applications so that the foreign one expires just before the British one, and when one renews the British one, the other is expired and needn't be sent to the Home Office. Et voilà. Are you with me?