mtx <- matrix(1:16,4)
dimnames(mtx)[[2]][1] <- 'col1'

mtx <- matrix(1:16,4)
dimnames(mtx)[[1]] <- letters[1:4]
dimnames(mtx)[[2]] <- LETTERS[1:4]
dimnames(mtx)[[2]][1] <- 'col1'
dimnames(mtx)[[2]][2] <- 'col2'

mtxNameSticker <- function(mtx, prepend = NULL, MARGIN=2)
{
    if (MARGIN == 1) max <- nrow(mtx) else
        max  <- ncol(mtx)
    if (is.null(prepend)) if (MARGIN == 2) prepend <- 'C' else
        prepend <- 'R'
    if (length(prepend) == 1) prepend <- paste0(prepend, 1:dim(mtx)[[MARGIN]])
    dimnames(mtx)[[MARGIN]] <- seq(from=1, by=1, length.out=dim(mtx)[[MARGIN]])
    for (i in 1:max){
        dimnames(mtx)[[MARGIN]][i] <- prepend[i]
    }
    return(mtx)
}

dimnames(mtx) <- lapply(dim(mtx), seq_len)
mtx
#   1 2  3  4
# 1 1 5  9 13
# 2 2 6 10 14
# 3 3 7 11 15
# 4 4 8 12 16

dimnames(mtx)[[2]][1] <- 'col1'
mtx
#   col1 2  3  4
# 1    1 5  9 13
# 2    2 6 10 14
# 3    3 7 11 15
# 4    4 8 12 16

R> M <- matrix(1:4,2,2)
R> M
     [,1] [,2]
[1,]    1    3
[2,]    2    4
R>

R> M1 <- M; dimnames(M1) <- list(NULL, c("a","b")); M1
     a b
[1,] 1 3
[2,] 2 4
R>

R> M2 <- M; dimnames(M2) <- list(c("A","B"), NULL); M2
  [,1] [,2]
A    1    3
B    2    4
R>

x <- NULL
x[[2]][1] <- 'col1'
str(x)
##  chr [1:2] NA "col1"

x <- NULL
x[[2]][1] <- 'col1'
str(x)

## List of 2
## $ : NULL
## $ : chr "col1"

dimnames(mtx) <- list(character(nrow(mtx)), character(ncol(mtx)))
# or
# dimnames(mtx) <-  lapply(dim(mtx), character)
dimnames(mtx)[[2]][1] <- 'col1'

dimnames(mtx) = list(NULL,col1=NULL)
mtx
#      col1
#       [,1] [,2] [,3] [,4]
#  [1,]    1    5    9   13
#  [2,]    2    6   10   14
#  [3,]    3    7   11   15
#  [4,]    4    8   12   16