domain count
1                                START OF NEW FILE
2                                        94_res.txt
3                                         google.ru     2
4                                START OF NEW FILE
5                                        95_res.txt
6                                search-results.com     2
7                                            hpc.ru     1
8                                  theadgateway.com     1
9                                         google.by     6

transform(test.df,
          fnameRaw = ifelse(lag(test.df$domain, 1) == "START OF NEW FILE ",
                            test.df$domain,
                            ""))
                                             domain count           fnameRaw
1                                START OF NEW FILE        START OF NEW FILE
2                                        94_res.txt
3                                         google.ru     2
4                                START OF NEW FILE        START OF NEW FILE
5                                        95_res.txt
6                                search-results.com     2
7                                            hpc.ru     1
8                                  theadgateway.com     1
9                                         google.by     6

domain  count     fnameRaw    filename
1     START OF NEW FILE                             N/A
2            94_res.txt           94_res.txt  94_res.txt
3             google.ru       2               94_res.txt
4     START OF NEW FILE                       94_res.txt
5            95_res.txt           95_res.txt  95_res.txt
6    search-results.com       2               95_res.txt
7                hpc.ru       1               95_res.txt
8      theadgateway.com       1               95_res.txt
9             google.by       6               95_res.txt

library(dplyr)
library(zoo)

DF %>%
   mutate(filename = ifelse(lag(domain) == "START OF NEW FILE", domain, NA),
     filename = na.locf0(filename),
     filename = ifelse(domain == "START OF NEW FILE", NA, filename))

domain count   filename
1  START OF NEW FILE    NA       <NA>
2         94_res.txt    NA 94_res.txt
3          google.ru     2 94_res.txt
4  START OF NEW FILE    NA       <NA>
5         95_res.txt    NA 95_res.txt
6 search-results.com     2 95_res.txt
7             hpc.ru     1 95_res.txt
8   theadgateway.com     1 95_res.txt
9          google.by     6 95_res.txt

library(dplyr)

DF %>%
   group_by(g = cumsum(domain == "START OF NEW FILE")) %>%
   mutate(filename = c(NA, rep(domain[2], n()-1))) %>%
   ungroup %>%
   select(-g)

g <- cumsum(DF$domain == "START OF NEW FILE")
make_Filename <- function(x) c(NA, rep(x[2], length(x) - 1))
transform(DF, filename = ave(DF$domain, g, FUN = make_filename))

DF <- structure(list(domain = c("START OF NEW FILE", "94_res.txt",
"google.ru", "START OF NEW FILE", "95_res.txt", "search-results.com",
"hpc.ru", "theadgateway.com", "google.by"), count = c(NA, NA,
2L, NA, NA, 2L, 1L, 1L, 6L)), row.names = c(NA, -9L), class = "data.frame")