Register describes a type or style of a language used in different social settings. Speakers use different registers or styles in different social situations.
As found in languages around the world, register variation involves two general levels: formality and informality -- in formal and colloquial (or informal) contexts. Below gives a quick example in American Sign Language (ASL) on a formal/informal continuum.
Gloss or transliteration: that why..
English equivalent: that's why..
The demonstrative pronoun that in this ASL phrase is a formal citation.
On the other hand, the demonstrative pronoun that in this phrase is generally used in a casual conversation. Notice that the signer doesn't use a passive hand.
Martin Joos (1961) identifies five levels of registers: intimate, casual/informal, consultative, formal and frozen in spoken English. Based on this categorization, the videos below show examples of ASL registers or styles when a person introduces oneself in different social settings.
Intimate register is the level used by people in casual situations or among people who know each other well. E.g. family, life partners, etc.
Casual/informal level is similar to the intimate level except for use of private language in intimate contexts. It is used in informal gatherings.
Approximate gloss: me[indexing] jo.
Approximate English translation: i'm jo. or i am jo.
This type of register is used in informal contexts (e.g. party).
Consultative is a style used in everyday conversation between strangers, in a classroom, at workshops or meetings.
Approximate gloss: my name jo. or i am jo.
Approximate English translation: my name is jo.
This type of register is often used in semi-formal settings, such as academic lectures, business meetings, etc. It is also often used by some ASL natives who introduce themselves to English speakers who are ASL learners.
Formal is the level used for on-stage presentations, at banquets, etc.
Approximate gloss: me[honorific] jo.
This type of honorific reference is often used in formal contexts such as banquets, religious ceremonies, poetry, royal introductions, etc.
Lastly, frozen is used in religious ceremonies or services, courtroom, etc. The text is usually "frozen", such as anthems. A frozen text is not commonly practiced in ASL culture, like many other cultures.
In frozen and formal registers, signing is usually at slower pace and is clearer and fully executed in larger space.