Hi, what a good question to ask about signing name. I had experience students asking me similar and when they "can" get or create a sign name. Creating an sign name would give you an identity and you may become more motivated to learn more sign language. Signing name is very unique to deaf/ hoh community. I have two signing name. The one signing name I grew up using JA for whole of my life was given from my deaf parents who able identified my twin brother and I. His signing name "JT" means Justin and mine is "JA" means Jonathan. Just finger spell the word J.A. without (.) that was my signing name for almost 25 years of my life...but then I wanted to change new signing name is more descriptive than arbitrary. Four years ago, I went to France there are large deaf communities there using descriptive sign name rather than letter word signed name. I decided to change my sign name to "4" movement twice on my head it shows my hair spiked. I always had it that way for long time. It is my personality. I can help you with that if you want. I am good with giving people sign name. You can have more than one signing name and have a story to tell how you grown learning about language and deaf culture as you learn too.
There are two categories of signing name: arbitrary and descriptive. Quote "One category of name signs is called arbitrary and the other is descriptive. Arbitrary name signs are made up of common signs, typically made up using the first letter, for names that are used more widely within the Deaf community. While common and easily identifiable to others, arbitrary name signs are not necessarily "personalized" to each individual. In contrast to arbitrary name signs are the more unique or personalized name signs called descriptive name signs. Descriptive name signs can be more personalized to the individuals because the sign usually indicates some distinctive physical feature. Descriptive name signs can also be assigned based upon unique characteristics such as employment, characteristics of body movement, or personal tendencies. While both arbitrary and descriptive name signs are taken seriously within Deaf culture and are only given after collaboration, unlike a name on a birth certificate, name signs can change as a person ages." from lifeprint.com.