Counting unique / distinct values by group in a data frame

A data.table approach

library(data.table)
DT <- data.table(myvec)

DT[, .(number_of_distinct_orders = length(unique(order_no))), by = name]

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data.table v >= 1.9.5 has a built in uniqueN function now

DT[, .(number_of_distinct_orders = uniqueN(order_no)), by = name]

In dplyr you may use n_distinct to "count the number of unique values":

library(dplyr)
myvec %>%
  group_by(name) %>%
  summarise(n_distinct(order_no))