Yes, either a sample number if they are taken at fixed intervals and you know the start time or, more usually, the actual clock time the sample was taken. UNIX time is often used because it is easy to decode back to clock time/date and it has 1 second resolution.
By "time stamping" do you mean to attach a real time clock value or just an info which will help you to distinguish later which ADC data was acquired first?
You can have a sufficiently large counter that increments on the rising edge of the system clock. This will provide the unique time-stamp value. Now the freshly acquired ADC value will be in a buffer register. Have another sufficiently large buffer register such that large_buff_reg >= time_stamp_data + ADC_data.
On the rising edge of the system clock copy time_stamp_data + ADC_data to the large_buff_reg and your work is done!