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

Yes

The spelling, meaning, and grammatical category of the word "Guatemala" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. In Continental Portuguese, speakers tend to use "vowel reduction," meaning unstressed vowels (like the "a" sounds in the middle or end of the word) are more "closed" or clipped, making the word sound slightly shorter and more muffled to a Brazilian ear.

Brazilian Portuguese Examples

1. Eu quero viajar para a Guatemala. (I want to travel to Guatemala.)
2. A gente vai visitar a Guatemala nas férias. (We are going to visit Guatemala on vacation.)
3. Você já conhece a Guatemala? (Do you know Guatemala?)
4. A Guatemala é um país muito legal. (Guatemala is a very cool country.)
5. Eu vi um vídeo muito bonito sobre a Guatemala. (I saw a very beautiful video about Guatemala.)

Continental Portuguese Examples

1. Eu pretendo viajar para a Guatemala. (I intend to travel to Guatemala.)
2. Nós vamos visitar a Guatemala nas férias. (We are going to visit Guatemala on vacation.)
3. Tu já conheces a Guatemala? (Do you know Guatemala?)
4. A Guatemala é um país muito giro. (Guatemala is a very nice/pretty country.)
5. Eu vi um vídeo muito bonito sobre a Guatemala. (I saw a very beautiful video about Guatemala.)