Which characters typically occur only within names?
Chih-Hao Tsai's Technology Page is an excellent resource (with the caveat that the corpuses it uses are Taiwanese). On this page you can find frequencies of the most common characters used in surnames and given names.

Most common surnames (2012):

陳
林
黃
李
張
王
吳
劉
蔡
楊
許
鄭
謝
郭
洪
邱
曾
賴
廖
徐
周
葉
蘇
莊
呂

It's clear that this is from a Taiwanese source since 陳 is most common; if this were the mainland you'd expect 王 to be the most common.

Here's the list of most common characters in given names (2012); if you cross reference this with the list of most common characters, you get this:


庭 (rank 1447)
婷 (rank 2410)
宇 (rank 1159)
文 (rank 33)
佳 (rank 739)
雅 (rank 1112)
怡 (rank 1651)
家 (rank 66)
柏 (rank 1585)
冠 (rank 1023)
子 (rank 66)
廷 (rank 1834)
安 (rank 360)
翔 (rank 1503)
嘉 (rank 1056)
彥 (rank 1677)
宜 (rank 719)
瑋 (rank 2246)
軒 (rank 1698)
瑜 (rank 1854)
欣 (rank 943)
凱 (rank 1413)
君 (rank 767)
育 (rank 585)
萱 (rank 3029)


So you can see that apart from a few very common characters (like 文, 家 and 子), most of these characters are relatively uncommon outside of names. Keep in mind that characters that are common in given names also obviously show up in the list of most common characters, so anything above say rank 2000 may qualify as "name" characters. I'd say it's very hard to encounter the characters 婷, 瑋 or 萱 outside of names.

You can download the entire corpus and run your own analysis if you wish.

And here's the list of most common given names (note that most of these are two-characters long):

雅婷
雅筑
冠宇
冠廷
怡君
宗翰
佳穎
彥廷
家豪
柏翰
宜庭
郁婷
承翰
詩涵
宇軒
佳蓉
鈺婷
家瑜
怡婷
怡萱
詩婷
怡安
家瑋
郁雯
冠霖

So I wonder how many (thousands) of 陳雅婷 are in the world? :)