From a named list I want to create a two columns data.frame(), with list names appearing in the first column and list elements in the second. 
I managed to
Converting my comments to an answer, you can use stack from base R, or melt from "reshape2":
Here's stack:
head(stack(my_list), 15)
##    values        ind
## 1       0  one_digit
## 2       1  one_digit
## 3       2  one_digit
## 4       3  one_digit
## 5       4  one_digit
## 6       5  one_digit
## 7       6  one_digit
## 8       7  one_digit
## 9       8  one_digit
## 10      9  one_digit
## 11     10 two_digits
## 12     11 two_digits
## 13     12 two_digits
## 14     13 two_digits
## 15     14 two_digits
Here's melt:
head(melt(my_list), 15)
##    value         L1
## 1      0  one_digit
## 2      1  one_digit
## 3      2  one_digit
## 4      3  one_digit
## 5      4  one_digit
## 6      5  one_digit
## 7      6  one_digit
## 8      7  one_digit
## 9      8  one_digit
## 10     9  one_digit
## 11    10 two_digits
## 12    11 two_digits
## 13    12 two_digits
## 14    13 two_digits
## 15    14 two_digits
One difference between the two approaches is that melt will automatically create the "L1" column even if the list doesn't have names, and will work with nested lists too.
head(melt(unname(my_list)), 15)
##    value L1
## 1      0  1
## 2      1  1
## 3      2  1
## 4      3  1
## 5      4  1
## 6      5  1
## 7      6  1
## 8      7  1
## 9      8  1
## 10     9  1
## 11    10  2
## 12    11  2
## 13    12  2
## 14    13  2
## 15    14  2