The "Kardashian Kard" was a private label label card, just like the Wal-Mart CC and others, so, yes, when it still existed the CSR likely did identify themselves as "Kardashian Card" representatives. Private label cards are the norm for most retailers; it's their branding, even when you to talk to a live CSR, but it is managed by a 3rd party financial company. There are some retailers that do their own cards but these days they are the exception. Here's an article that deals specifically with
Synchrony.
Now as to why a Wal-Mart CC purchase at Best Buy would tend to trigger a fraud alert, the answer would need to come from Synchrony Bank as to what their thresholds are. The only thing that would be interesting to find out is whether Synchrony uses the same threshold across all of their private label cards or whether they use different thresholds depending on who their co-brand partner is.
Now, of course, semantics doesn't really help with the situation you find yourself in but as was already pointed out, the Wal-Mart CC, even though it is issued & managed to Synchrony, is through MasterCard and their rules would indeed trump the others. In short, when you're dealing with "Wal-Mart CC" reps, you're really talking to either a Synchrony CSR or a 3rd party call center contracted by Synchrony (one phone call they might identify themselves as "Wal-Mart CC", the next call right after they might be "Lowes CC", and so on) and if you truly hit a brick wall in trying resolve a problem you could try reaching out to MasterCard directly (eg:
here's their policies for merchants).