Re: The "relationships" in contacts only has three options: spouse, manager and assistant as options
I'm having the same issue. #2/5 & #4 are missing the issue in different ways...
#2/#5: when selecting "add related name", and then tap on the default label ("manager") to change it, only "manager", "spouse" and "assistant" are shown as options. No other options, nor "Add Custom Label". See first three screenshots.
#4: He probably did investigate, and found this thread, like me. What you are suggesting is simply adding another number to a contact... That's just not what we want to do.
From one contact we want to refer to another, different, contact. So a referral to all information of the (spouse|daughter|whatever) and not just their phone number. This is normally done via "add related name" when editing the contact.
For instance: I may not remember the name of someone's spouse, but I still want to be able to look up her/his (birthday|address|whatever) without calling them.
But still, even if I wanted to only add the number to a contact: your suggestion doesn't work for me. And I think it's related: If I edit a contact's number as you suggest, there is no option "Add Custom Label" here either. See the other screenshots ("radio" is the last option, can't scroll down).
So what isn't working is (creating|displaying) any custom label... I believe that in my case it's because my contacts are synchronised with Exchange.
While trying some things I noticed that, when I create a new contact, and then -before saving it- attempt to change the label for either a number or a "related name", the "Add Custom Label" *is* there. However, as soon as I save the contact the custom labels are reset to the default for the field. Then, when editing it again, the option for a custom label is no longer present as with all other saved contacts.
Exchange probably doesn't support custom labels. It makes sense that if you sync your contacts with something that doesn't support them iOS would turn that functionality off. So this may affect different sync options (Google? surely not iCloud...). I don't know though since I only ever use Exchange.
There might be an option to create custom labels on the server end of whatever you synchronise contacts with, so you can then use them on the iPhone. I'm checking that out later.
Those that have this issue: are you synchronising your contacts? If so, with what?