data.frame with 2 columns with the same name: how to select the second one?

It is not advised to have duplicate column names and this is one of the main reason.

You can select column by position.

d3[[2]]

Or if you want to select them by name, here is another way -

d3[names(d3) == 'a'][[2]]

It is a little surprising that R does not throw an error/warning when you cbind 2 dataframes that have the same column names. Because, usually R dataframes do not allow exact same names (when you create them using data.frame()).

For example, if you try to create a dataframe (from scratch/without binding 2 dataframes) R automatically changes names slightly by adding .number starting from the second column:

data.frame(a = c(1, 2, 3), a = c(3, 4, 5), a = c(5, 6, 7))

  a a.1 a.2
1 1   3   5
2 2   4   6
3 3   5   7

Which means dataframes should not have the same column names. In your example, when you do d3$a R can only show you the first column that have the name a. Similarly, if you do d3[,"a"] you get the first column with the name a.

In general, it would not be a good idea to have a dataframe with multiple columns with the exact same names. However, if you really need to have such a dataframe and you have to get the second column, you would need to do something like:

d3[, 2]

[1] 3 4 5

you may make use of library janitor here

d1 <- data.frame(a=c(1,2,3))
d2 <- data.frame(a=c(3,4,5))
d3 <- cbind(d1,d2)

janitor::clean_names(d3)
#>   a a_2
#> 1 1   3
#> 2 2   4
#> 3 3   5

^{Created on 2021-05-22 by the reprex package (v2.0.0)}

We can also do match

d3[match('a', names(d3))][[2]]