Setting all APs in one network to same ESSID is exactly wbat you should do and for half-reasonable APs that works well.

Big name brand vendors will sell you APs that support some proprietary coordination mechanism between them (usually with central "wireless network controller" as separate device), but that is not required for roaming to work. Such solutions (apart from centralized management) are mostly to keep your APs from interfering with each other (which is non-issue unless you have more than three and unless they are placed in unfortunate physical locations).