Can a player use a split card's other half to determine if a card shares a name for legend rule purposes?

Split cards have two distinct names — one for each half. The Legend Rule (CR 704.5j) checks whether two permanents a player controls share a name. For split cards, CR 708.3 is the key rule: while a split card is on the stack, it has the characteristics of both halves. However, once a split card resolves and exists as a permanent on the battlefield, only the characteristics of the face-up half that was cast apply — unless it somehow has both halves relevant (which doesn't typically occur on the battlefield for most split cards).

For naming purposes specifically, CR 708.3 states that while a split card is a spell on the stack, it has both names. But on the battlefield as a permanent, a split card only has the name of the half that was cast (or, for meld and fuse, the relevant combined form). So a legendary permanent that is one half of a split card only has that half's name on the battlefield.

This means you cannot use the other half's name to dodge the Legend Rule, nor can the other half's name cause the Legend Rule to trigger. If you control a legendary permanent named 'Fire' (one half of 'Fire // Ice'), and your opponent controls a legendary permanent also named 'Fire // Ice' cast as 'Ice,' these do NOT share a name on the battlefield — one is 'Fire' and one is 'Ice.'

Example: Suppose 'Appeal // Authority' were legendary (hypothetically). If you cast and resolve 'Appeal,' the permanent on the battlefield is named 'Appeal.' A second legendary named 'Authority' entering the battlefield would NOT trigger the Legend Rule, because 'Appeal' ≠ 'Authority,' even though they are on the same physical card.

In summary, the other half of a split card is irrelevant for legend rule name-checking once the card is a permanent on the battlefield. Only the cast half's name applies in that zone per CR 708.3 and CR 201.5.