in heaven's name
You can use in heaven's name in questions beginning with 'what', 'when', 'who', 'why', and 'how' to add emphasis in a way that shows that you are very angry or surprised .
for God's sake, for goodness sake, for heaven's sake
Some people use expressions such as for God's sake, for heaven's sake, for goodness sake, or for Pete's sake in order to express annoyance or impatience, or to add force to a question or request. The expressions 'for God's sake' and 'for Christ's sake' could cause offence.
https://www.collinsdictionary.com/dictionary/english/heaven/...As we can see, these two expressions convey different feelings.
Pelo amor de Deus is usually translated as
For God's sake, which may be offensive for some. According to Collins, it's used to express annoyance or impatience whereas
in heaven's name expresses anger or surprise. The choice of the right translation will depend on further context and other verbal as well as non-verbal cues, such as tone of the voice, circumstances in which the phrase was uttered, etc.