Is the word namorados the same in Brazilian and European Portuguese?

No.

While the spelling and core meaning of "namorados" are identical in both dialects, there are differences in grammar and syntax (typical usage). In Brazil, it is common and natural to omit the definite article before possessive pronouns (e.g., meu namorado), whereas in Portugal, the article is typically required (o meu namorado). Additionally, the construction of continuous actions differs: Brazilians use the gerund (namorando), while Portuguese people use the preposition "a" followed by the infinitive (a namorar). There is also a difference in pronunciation, as Brazilian Portuguese tends to reduce unstressed vowels (pronouncing the final "os" more like "us"), whereas Continental Portuguese maintains more distinct vowel sounds.

Brazilian Portuguese

1. Eu e meu namorado vamos ao shopping. (My boyfriend and I are going to the mall.)
2. Eles são namorados há muito tempo. (They have been dating for a long time.)
3. Você tem namorado? (Do you have a boyfriend?)
4. Meu namorado está trabalhando agora. (My boyfriend is working right now.)
5. Eles estão namorando desde o verão. (They have been dating since the summer.)

Continental Portuguese

1. Eu e o meu namorado vamos ao shopping. (My boyfriend and I are going to the mall.)
2. Eles são namorados há muito tempo. (They have been dating for a long time.)
3. Tens namorado? (Do you have a boyfriend?)
4. O meu namorado está a trabalhar agora. (My boyfriend is working right now.)
5. Eles estão a namar desde o verão. (They have been dating since the summer.)