Transforming Tabular Data

I need help transforming the following dataset (table) into the attached screenshot I've provided. Notice the difference is that the dataset I need has the new column with the necessary variables.

What have you done so far and what problems did you run into?

I would like to transform this data so that a new column is made with a new header and the row names as listed under this new column. I am trying to use tribble function but unsure what to begin the code with before as_tribble(X). Looking online I see that I would need as_tribble(df, rownames = "name"), but it gives an error?

dplyr::as_tibble(neuraldata,rownames = "TIME")
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