One of the key words or themes used throughout the franchise is that of connection. Sora's social self, as connected, survives/triumph's; Riku's individual self must be tempered with social connects; the worlds must be separated, must not be connected; memories are connected; people are connected through memories and hearts.
The word used in Japanese is 繋ぐ. The only instance it strays is during Chain of Memories when talking about how memories are 鎖, chains. However, like the idea of chains of iron and gold, chains in this way can be shackles or they can be lifelines. Whereas the Nobodies indicate that memories are shackles, or rather memory is a shackle (記憶の鎖), the good social subject Sora holds them as lifelines.
The English words used are link, connect, tie and chain. While there is no particular added meaning in any of these terms, and in fact the dual meaning of chain brings out Chain of Memories' theme far better than 鎖, the breadth of words does not in fact hammer in the concept, both good and bad, of connection.