You don't need to do anything - they will grow on and make a very interesting multi stemmed Cordyline - if there are too many, you can remove some and leave the ones you want. If you didn't already cut down the main stem of the original plant, do that.

The new shoots around the stem means there is another growth coming so just watch it come up, it will be beautiful, I have three in my garden, one of them is ten foot high, mine are at the moment displaying new leaves so am expecting new growth soon, I pull off the old wilting leaves when they hang down cause I like looking at the stem too, hope this helps, enjoy.