Although not required I recommend it. The reason I recommend it is because if the FAA does do a long book review that at least has more credibility that some one's name that could've just been penciled whipped in. At ATP we always logged the certificate numbers, also make sure you don't log actual IMC time as you are suppose to be under the hood. We had a bunch of guys get in deep doo doo with the examiners are on that one. To save yourself the trouble always remember you are both PIC's but the safety pilot can't log anything but TT and PIC time. Every thing else would be credited towards the PF who is acting as PIC.