First of all, we do not have specific dates as your culture does. We observe the moon-cycles and seasons, and some even notice the solstice and equinox, but most days pass simply, as only days. When a child is born, we might mark the day by some significant event--the first rainstorm of spring, or the cutting of hay, and if special gifts were given, it would be when that day comes again.
But it seems to me that there is a significant flaw in your culture's way of doing things. Do you only honor the person on this day, or all year round? If you honor them all the year round, why bother with one particular day? Perhaps the closest ceremony we have is when a child's rose deepens hue and remains blossoming all winter, for then the child is a baby no longer, but a young one learning the ways of the King.