The problem here is in believing the casino is your friend.
WRONG, they are after your money. Reputable ones will be satisfied with the long term house advantage, and their confidence in their promotions. They will honour their own mistakes.
Less reputable outfits will treat any mistake as a "deliberate act", and will uphold any terms that allow them to pay less. In this case, they were happy to accept your deposits despite the fact it would only need a simple software check to discover the difference in names, had you lost, you would never have known this was a problem. It may even be that had you withdrawn less than total deposits on that card they would have been happy to pay, but when players come out ahead the full set of tests are done.
Sadly, this leaves halifaxplayer trussed up like the proverbial Christmas turkey, ready to roast. eCogra would side with the casino on this, as this is a breach of the terms about allowing others to use your account.
Further evidence would show whether this was genuine play, but I don't expect the casino are interested as they can save themselves $800.
You could try a PAB, but you may not get the answer you seek. I do not know if the rep is still active here after they got into "not recommended" due to over zealous actions last year over multiple account frauds.