Hey there, I don't think so. Which emblem (if it's a specific one?). Emblems will generally be tied to Collections, which shouldn't be affected by cross-save, or linked to your Bungie Account, cross-save shouldn't affect this either assuming you only have one. The emblems that may have an issue are preorder ones, they will only be available while playing on the owning platform - a preorder emblem earned by buying something on Steam, will only be available while playing on Steam, you would not be able to access it while playing the same characters cross-saved to PSN.