Is there a single sign for the name Jennifer?
No, there is no universal sign for the name Jennifer. Like most proper names, it is fingerspelled. A specific person named Jennifer might have a personal 'name sign' given to her by Deaf friends, but you would still fingerspell her name when first introducing her.
How do I sign the double 'N' in Jennifer?
To indicate a double letter in ASL, you don't need to form the letter twice from scratch. Instead, form the 'N' handshape and either give it a gentle bounce or slide it slightly outward to the side.
Do I have to fingerspell my name every time?
Yes, when introducing yourself to someone new, you should always fingerspell your name. If you have a name sign, you would fingerspell your name first, and then demonstrate your name sign.