@kkrupka From what I understand, Square is the merchant of record, and the transaction will always show as SQ *<business name>.  I do think the business name is truncated at times.  I am not sure if the online store has a different nomenclature versus the app etc.

I have generally found that any "keyed" transaction aka manual entry or card not present will represent the highest chance of fraud rate etc.  The best advice is to always swipe or dip cards if you can.  Most often this has little to do with square and more to do with the algorithms and policies of the card holders bank.  This may not answer your question, but just wanted to give you a little insight into how the behind the scenes works for me.  There are a ton of variables that can trigger things like this.