When creating a character in Phantasy Star Online, the game will assign a "Section ID" to your character. This value is determined by your chosen name. Each character in the string advances the cipher by a unique amount. When playing the PC version, or Blue Burst, this process is more complex - it uses a slightly different cipher and adds an additional offset based on your chosen class. Thus, for this reason, it is highly unlikely that a Dreamcast name will result in the same Section ID on Blue Burst.
Section IDs influence the drop rates of certain items, allow certain special items to drop, and also affect the list of possible Mags that a given character may obtain through evolution. A complete breakdown of the cipher can be found here.