That post seems to be just about your number when (if) you look it up in the settings, rather than about other contacts. So I think it's something different.
(In fact I've done what they say, bought a new phone and transferred my number tp a new SIM without seeing that problem - once you get a SIM update the number in the settings updates as well. Unless Samsung specifically screwed that up in some phones...).
As for your issue, is there anything these contacts have in common, e.g. you store them on your SIM, or on your phone without syncing them, they are in a particular contact to group, linked to a particular account...? Anything different about these might help identify the cause, and hence (hopefully) solve the problem.
I guess another question is what happens if you just open one and edit it? Presumably you can tell who it is from the information inside it, so what happens if you just add a name by hand?