Thank you Dave2e for mentioning lunar-package.
So the solution is:
library(tibble)
library(dplyr)
library(lubridate)
mycal <- tibble(datum=(seq(as.Date("2020/01/01"), as.Date("2025/12/31"), "days")))
library(lunar)
mycal %>% mutate(moon=lunar.phase(datum, name=T) %>% as.character())