Hi! It seems like you are following the old documentation. The new docs are available here: Datasets — datasets 1.17.0 documentation (this is an example with to_tf_dataset: Train with 🤗 Datasets — datasets 1.17.0 documentation).

I am uncertain if label_cols can be used to specify labels for differently named columns, or if it only possible to pass labels with a column named label inside the columns parameter?

Yes, label_cols supports columns not necessarily named label.
cc @Rocketknight1