Do not use assign until you are an experienced R programmer (and then you will need it very rarely). Here you could pre-allocate a matrix and fill it. The columns will correspond to your samples:
numOfsam <- 3
length <- 5
mu <- 2
sigma <- 0.1
result <- matrix(nrow = length, ncol = numOfsam)
set.seed(42) #for reproducibility
for (i in seq_len(numOfsam)) {
result[,i] <- rnorm(length, mean = mu, sd = sigma)
}
result
# [,1] [,2] [,3]
#[1,] 2.137096 1.989388 2.130487
#[2,] 1.943530 2.151152 2.228665
#[3,] 2.036313 1.990534 1.861114
#[4,] 2.063286 2.201842 1.972121
#[5,] 2.040427 1.993729 1.986668
Of course you can get exactly the same result without a for loop:
set.seed(42) #for reproducibility
result2 <- matrix(rnorm(length * numOfsam, mean = mu, sd = sigma), ncol = numOfsam)
result2
# [,1] [,2] [,3]
#[1,] 2.137096 1.989388 2.130487
#[2,] 1.943530 2.151152 2.228665
#[3,] 2.036313 1.990534 1.861114
#[4,] 2.063286 2.201842 1.972121
#[5,] 2.040427 1.993729 1.986668