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I realize that there may be a language barrier here. But I really do not understand what "took his name" means. You need to explain that in more detail. Did she call out his name while you were being...

What I took that to mean was she called him by that guy's name while they were being intimate.

Did she call out this guy's name while you were being intimate? That's what isn't clear from your post. If she did, I can understand you being upset. Otherwise, this is something that happened before...