fct_reorder() is the function you want (reorder a factor by another variable), but the issue in your plot is that you're mapping the wrong variable to the y-axis. Try this:
ggplot(test, aes(fct_reorder(Name, Number), Number)) +
geom_col()
geom_col() expects the y-axis to be a number, and you were mapping it to a reordered factor (look at the values on your axis, you're lining up A with A, B with B, etc.