The reason for the name isn't something you'd tell kids on the first day, but having reasonable names for things makes the going easier later on. Nameless ones behave like the bingo chips or whatever from learning integers, and like the bears the kids counted in kindergarten. One of them stands for 1, and five of them stands for 5. If you are using the cutout ones, they are one square centimeter, and you can make a connection to measurement if you want. Settle on names within groups, and within the class.
Naming conventions are important to mathematical communities.
It's OK to give these the same names because they are used in the same way. The point to emphasize with names is not that there's a correct name for each piece, but that we need names to be able to talk about them. Collections, part 1 Make a collection of pieces, using all three kinds, and write down its name. Settle on a convention for writing collections which shows that all the pieces are added together in one collection. Abbreviations might help.