In Chrono Trigger, Ted Woolsey changed the Grand Lion's name to the Masamune; thus, Grand and Lion became Masa and Mune. He also mistranslated Dream's name as "Doreen." For some reason, though, he didn't make the same mistake, nor did he change Grand's name, when it came to the triple tech Grand Dream. Grand Dream is also the name of Serge's ultimate weapon, although it was called the "Mastermune" in the translation of CC. I guess the bottom line was that certain things could sometimes retain their good original names, but only until they actually became important to the plot.

So, Dream did indeed join up with Grand and Lion in CT. It was just in the form of a triple tech rather than that of a weapon.