In Portuguese, as in English, there are suffixes used to denote nationality. There is no need to capitalize these words, unless they appear at the beginning of a sentence. We use Nacionalidade to refer to the country where a person was born, and Naturalidade to refer to the city or state where a person was born. Here are some examples: Here are some of them.
EIRO is a very unusual ending for nationalities. Its origin comes from someone being a hard-working person. Back in colonial times, the Portuguese referred to Brazilians as BRASILEIRO because they were the work force there. The same logic applies to the Portuguese term for miners, MINEIRO, which is also how we call people from Minas Gerais. Minas Gerais is a region with many mines that was largely inhabited by miners, and so the EIRO ending is used.