Here’s a shorter way, taking advantage of the way unlist
deals with names:
library(dplyr)
df1 %>% group_by(Name) %>% do(as_tibble(t(unlist(.[2]))))
# # A tibble: 2 x 4
# # Groups: Name [2]
# Name MedName1 MedName2 MedName3
# <chr> <chr> <chr> <chr>
# 1 name1 atenolol 25mg aspirin 81mg sildenafil 100mg
# 2 name2 atenolol 50mg enalapril 20mg <NA>