To obtain your required format i.e., 2016-month-day , you can use format function once you have converted vector of strings to Date type.
I hope below code snippet clears your doubt.
> d = c("2016-02-08","2016-02-18","2015-02-08","2016-02-02")
> class(d)
[1] "character"
> d = as.Date(d)
> class(d)
[1] "Date"
> d = format(d,"%Y-%b-%d")
> d
[1] "2016-Feb-08" "2016-Feb-18" "2015-Feb-08" "2016-Feb-02"
Format function converts the date type objects into the required format. Refer to this link for more information on date type formatting.