I had the same problem. Just changed the length of my putter in Garmin connect, sync-ed and then I could see the putter also on my S60. Sometimes I wonder if this SW engineers ever test their work???
I fixed the issue of my wedges, and putter not showing up on the club sensor list by editing the default name on the gear list on the garmin connect web page as the thread suggested on my garmin s62 watch. Thank you for posting this, I was very disappointed that I was unable to add my clubs with the CT 10 sensors yesterday before my round of golf.
I had been having similar problems - after some time I’ve found the issue, I had too many clubs in my ‘Gear’, remove any clubs that aren’t actually assigned to anything ( my connect had duplicates of every club ), re sync and your watch should have the all the clubs on it.
Had the same issue with my putter. I deleted a heap of clubs, eg. 58 chip, 54 chip, 58 bunker, etc and tried pairing again and it worked straight away. You just can't have too many clubs in your My Bag.
I believe the limit is 26 clubs. I've discovered this by trial and error.