Using table
:
library(magrittr)
myvec %>% unique %>% '['(1) %>% table %>% as.data.frame %>%
setNames(c("name","number_of_distinct_orders"))
# name number_of_distinct_orders
# 1 Amy 2
# 2 Dave 1
# 3 Jack 3
# 4 Larry 1
# 5 Tom 2