HM Passport Office will place this observation in your passport when your name in your British passport is different to the name in your other nationality passport, and it is believed to be difficult or impossible for you to change the name in the other nationality documents to match your official name in your British documents.
Section 6 in Annex A: use of names in passports of UK change of name guidance for official documents covers this scenario in depth and you may wish to read it in its entirety; the sections most pertinent to your question are:
6.5 There are individual categories of applicant who may experience restrictions on their ability to meet the identity requirements of one name for all official purposes. These are primarily people who have dual nationality and who hold, have held or can obtain in the future a passport issued by another country.
6.6 Subject to the applicant being able to satisfy the following requirements, a passport may be issued in the name requested even where it differs from the name on the passport issued by another country. The following categories may be given exceptional consideration:
i. The law in the applicant’s country of origin restricts or prevents a change of name. Where there is such a restriction, the applicant will be required to provide evidence from their country of origin that a change of name is not permissible;
ii. The country of origin does not permit dual nationality meaning alignment of documentation will not be possible, the applicant will be required to provide confirmation from the country of origin that their citizenship has been cancelled;
iii. Where there is a requirement for the person to travel to their country of origin in order to change their name, and due to exceptional circumstances in their country of origin, they would be placed at a high level of risk;
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6.7 In the case of points (i) and (iii) above, a (British) passport may be issued and an observation placed in the passport saying: “The holder has a [country] passport, number [ ] issued on [date] in the name of [ ]. This passport is due to expire on [date].”
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6.13 The British passport will not routinely contain an observation of other passports held by a dual national unless by exception (see paragraph 6 above) it is in a different name. It is a matter for the passport applicant to raise at the point of application whether providing details of existing or previous overseas passports causes any particular concern.
My guess would be that you have two surnames (apellidos) in your other nationality and that the name the UK considers your official name lacks one or more of those names.
