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

Yes

The spelling, meaning, and grammatical function of "organizamos" (the first-person plural of the verb organizar) are identical in both Brazilian and Continental Portuguese. The only differences are phonetic: Brazilian Portuguese tends to have more open vowels and a more syllable-timed rhythm (where each syllable has a similar duration), while Continental Portuguese features more closed vowels and a stress-timed rhythm (where unstressed syllables are more heavily reduced or "swallowed").

Brazilian Portuguese Examples

1. Nós organizamos a festa de aniversário. (We organize the birthday party.)
2. Organizamos nossos arquivos mensalmente. (We organize our files monthly.)
3. Nós organizamos um jantar para a família. (We organize a dinner for the family.)
4. Organizamos nosso tempo de estudo. (We organize our study time.)
5. Nós organizamos nossa agenda semanal. (We organize our weekly schedule.)

Continental Portuguese Examples

1. Nós organizamos a festa de aniversário. (We organize the birthday party.)
2. Organizamos os nossos arquivos mensalmente. (We organize our files monthly.)
3. Nós organizamos um jantar para a família. (We organize a dinner for the family.)
4. Organizamos o nosso tempo de estudo. (We organize our study time.)
5. Nós organizamos a nossa agenda semanal. (We organize our weekly schedule.)