I think it is really interesting that as the name Jasper loss popularity, it never bottomed out. Even at its lowest value it was still being used and now it is back on a resurgence. It seems that this resurgence may be tied to the release of the Twilight novels where one character is named Jasper Hale. Soon after the release of twilight the name Jasper jumped in popularity and instead of dropping after a few years continued to increase most likely due to the creation of the twilight movies.

# Load packages
library(ggplot2)
library(dplyr)
library(babynames)

# Compute counts/proporations for "Other" names
other <- babynames %>% 
  group_by(year, sex) %>% 
  summarise(sum_n=sum(n), sum_prop=sum(prop)) %>% 
  mutate(
    total = sum_n/sum_prop,
    name = "Other",
    prop = 1-sum_prop,
    n = prop * total
    ) %>% 
  select(year, sex, name, n, prop)

# Add "Other" names to babynames
babynames <- babynames %>% 
  bind_rows(other) %>% 
  arrange(year, sex, desc(n))
baby_name <- "Jasper"
baby_sex <- "M"

single_name <- babynames %>% 
  filter(name==baby_name & sex==baby_sex)

ggplot(data=single_name, mapping = aes(x=year, y=prop)) + 
  geom_line() +
  xlim(c(1880, 2014)) +
  ylim(c(0, NA)) +
  xlab("Year") +
  ylab(paste("Prop. of ", baby_sex, " born with name ", baby_name, sep=""))