If a player has two legendary permanents with the same name and one phases out does the legend rule apply?

The legend rule (CR 704.5j) is a state-based action that checks whether a player controls two or more legendary permanents with the same name. If that condition is true, the player keeps one and the rest are put into the graveyard.

However, CR 702.108d states that phased-out permanents are treated as though they don't exist for purposes of game rules and effects. This means a phased-out permanent is simply invisible to state-based action checks, including the legend rule.

So if you control two legendary creatures with the same name and one phases out, the game only 'sees' one legendary permanent under your control. The legend rule condition is no longer met, and no legendary permanent is sacrificed. When the phased-out permanent phases back in, the legend rule will be checked again immediately as a state-based action.

Example: You control two copies of Thalia, Guardian of Thraben. Normally, you'd have to put one into the graveyard. But if one copy phases out (due to Vanishing or a similar effect), the game treats it as nonexistent, so you keep the in-play Thalia with no legend-rule trigger. When the phased-out Thalia phases back in, state-based actions are checked, and you must then put one copy into the graveyard.