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

Yes

The word "venho" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. It is the first-person singular present indicative of the verb vir (to come). The only difference is in pronunciation. In Brazilian Portuguese, the vowels are typically more open and the nasalization of the "en" is more pronounced and melodic. In Continental Portuguese, the vowels are often more closed, and the "e" in "venho" may be significantly reduced or nearly silent depending on the regional accent. Additionally, while the word "venho" itself does not change, the syntax (the way the word is used in a sentence with other words) differs, particularly regarding the placement of object pronouns.

Brazilian Portuguese Examples

1. Eu venho te ajudar com a mudança. (I am coming to help you with the move.)
2. Eu venho buscar você amanhã. (I am coming to pick you up tomorrow.)
3. Eu venho sempre aqui no final de semana. (I always come here on the weekend.)
4. Não venho mais te incomodar. (I am not coming to bother you anymore.)
5. Eu venho te encontrar na estação. (I am coming to meet you at the station.)

Continental Portuguese Examples

1. Eu venho ajudar-te com a mudança. (I am coming to help you with the move.)
2. Eu venho buscar-te amanhã. (I am coming to pick you up tomorrow.)
3. Venho sempre aqui ao fim de semana. (I always come here at the weekend.)
4. Não venho mais incomodar-te. (I am not coming to bother you anymore.)
5. Eu venho encontrar-te na estação. (I am coming to meet you at the station.)