usage - What connotation does the ending -n to a Japanese female name have?

The Japanese female names that end with "i" can be altered by adding "n" in their end. E.g.:
"Konami" -> "Konamin"
"Mizuki" -> "Mizukin"
"Narumi" -> "Narumin"

"Chinami" -> "Chinamin"
I would like to understand what exact connotation this alternation has. Under what circumstances could I call a person by that altered name? Would that infer any of my feelings to that person? Could that person not desire to be called by that name in the presence of the other people while considering it fine to be called by such name when having a private conversation? If yes, then why?

Answer

There are two "different" usages of the suffix 「ん」 in question.

Type #1: When the final 「ん」 is included in the girl's "official" nickname.

This means that the girl is already known to others by the nickname of 「～～～ん/ン」; therefore, practically everyone who knows her addressess her by that nickname.

In this usage of 「ん」, there is little to no connotation involved. It is just part of her nickname and no one would think anything of it (including the girl herself) as there is no reason to.

I would, however, not forget to mention the cuteness factor that the extra ん-ending creates in the Japanese ear.

Type #2: When the final 「ん」 is attached only by a limited group of people.

This is obviously the case that you are referring to where only a small group of close friends and family address her with a 「ん/ン」 attached to her original given name.

In this case, all kinds of connotation can come into play. You SHOULD NOT address the girl using the ん-ending just because you have seen/heard another person doing so.

This usage is a clear sign of affection, deep friendship, love, etc. Some girls actually let only their boyfriends use the ん-ending and do so only in their private conversations as well. As you probably know, affection, whether it is verbal or physical, is generally not displayed in public in the Japanese-speaking world.

In conclusion, one needs to know which of the two types of 「ん/ン」 it is before actually addressing a girl. Notice that it is the same for both Japanese-learners and us native speakers. You could end up really embarrassing all involved including yourself if you used this "suffix" incorrectly.

If you are not sure whether you do or do not belong in the group that could use the suffix with a ceratin girl, do not use it just yet. Spend some time around her and her friends and find out if it is the public 「ん」 or private 「ん」. Or you could ask one of her friends.