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

Yes

The only difference between the word "Luís" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazilian Portuguese, the "s" at the end of the name is typically pronounced as a voiceless alveolar sibilant [s], similar to the "s" in the English word "sun." In many dialects of Continental Portuguese, that same "s" is pronounced as a voiceless postalveolar fricative [ʃ], similar to the "sh" in "shoe." Additionally, Brazilian Portuguese tends to feature more open and clearly articulated vowels, whereas Continental Portuguese often features more closed or reduced vowel sounds.

Brazilian Portuguese Example Sentences

1. O Luís está fazendo o dever de casa. (Luís is doing his homework.)
2. Eu vi o Luís no shopping. (I saw Luís at the mall.)
3. O Luís é um cara muito legal. (Luís is a very cool guy.)
4. Onde o Luís guardou o celular? (Where did Luís put the cell phone?)
5. Você já falou com o Luís? (Have you already spoken to Luís?)

Continental Portuguese Example Sentences

1. O Luís está a fazer os trabalhos de casa. (Luís is doing his schoolwork.)
2. Eu vi o Luís no centro comercial. (I saw Luís at the shopping center.)
3. O Luís é um tipo muito porreiro. (Luís is a very cool guy.)
4. Onde é que o Luís guardou o telemóvel? (Where is it that Luís put the mobile phone?)
5. Já falaste com o Luís? (Have you spoken to Luís?)