In the American Deaf Community, there are certain traditions associated with naming. Deaf parents typically assign their children sign language names, sometimes even before they assign them hearing culture names. As adults, both Deaf and hearing, enter the Deaf community, core members of theDeaf community sometimes give sign names to them.
These "name signs" have been researched and were found to have followed specific rules. For a detailed description of these rules and a baby sign name dictionary, see Samuel Supalla's book, "The Book of Name Signs: Naming in American Sign Language".
Name signs tend to fall into three general categories: Arbitrary Name Signs (ANS), Descriptive Name Signs (DNS), and comination name signs.
Here is a video (in ASL) that explains some of the research:
Arbitrary Name Signs are always initialized, that is, they will take a handshape of one or two of the 25 letters of the alphabet (typically excluding Z, which has three movements).
ANS will take one of three movements:
Descriptive Name Signs are never initialized. They typically resemble a classifer, although sometimes they will resemble a sign. DNS may be assigned based on a number of characteristics, for example:
If a person has a name that is five or less letters ("Amy", "Tim", "Danny", "Billy"), the community might choose to spell that person's name in lieu of assinging a sign name to that person. Otherwise, members of the Deaf community will usually have one of the above types of sign names.
In some circumstances a person may have a name sign that does not follow either of these rules, but is a combination of the two types.
Combination Name Signs combine aspects of both ANS and DNS name signs. Combination name signs are initialized signs—that is, they are ASL signs, but the handshape is changed to the first letter othe person's name.
Sometimes, these are meant to be funny. There is a long history in poetry and storytelling where Deaf people assign combination sign names to famous hearing people who are not members of the Deaf community. For example: Richard Nixon, has been referred to as LIAR-with-N. Clinton was referred to as CHEATER-with-C.
Other times, a person may be given a combination name sign as a provisional sign name, that is, it lets people know that the person who has the name sign is new to the Deaf community.
There is one more reason a person might have a combination name sign. Sometimes people who don't understand the rules of name signs mistakenly give a name sign to a person. Some hearing professors of sign langauge, interpreters, or teachers give sign names without realizing they are in violation of Deaf culture traditions.
For a more detailed discussion of name signs and to view a dictionary of example name signs, see the book by Samuel Supalla, "The Book of Name Signs: Naming in American Sign Language".