Yes, this is gluten free
Tamari is traditionally brewed with little or no wheat, and tamari sold as gluten-free is a genuine substitute for soy sauce. Coconut aminos contain no soy or wheat at all.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and whether it has been recalled. 360,000+ packaged foods are already read and waiting.
The aisle guides below cover Tamari in context — which is usually the more useful question, because an ingredient rarely appears alone.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.