It's a Deaf social norm to share information like what kind of school you attended (hearing/deaf/ mainstream etc), if anyone in your family is Hoh or Deaf etc ...
I understand that you might not want to share intimate details of your life, however sharing basics (school, any Hoh/Deaf family members, how you got interested in ASL etc) is something that ALL Deaf people are going to ask ... and they aren't really going to open up or talk to you much if you say "sorry, not sharing" (it's just considered very rude)
What is the reason you're learning ASL ? Do you have a child/family member who's Hoh/Deaf ? Are you wanting to work with Deaf Children? Or be an interpreter ??
If your going to be an interpreter - the Deaf community is going to want (and need) to know who you are... I can't imagine working with an interpreter who told me "I'm not telling you anything about why me, as a hearing person got interested in ASL and became an interpreter" - honestly, as a client that would shoot up BIG RED FLAGS and I'd never hire them for anything other than very "public interpreting" (versus appointments for drs, lawyers, or anything that involved me saying anything -via the interpreter- about myself to the dr/lawyer/employer etc via)
Do you have privacy issues (stalkers, witness protection etc ?) if so ... interpreting is probably a bad idea as you'll be in all sorts of public situations and you're name and image may/will be "out there" (espeically in cases of VRS, or Virtual Interpreting etc.
The Deaf community isn't expecting for you to share your street address, the type of underwear you wear (or don't), etc ... however they will expect that you'll share some basics, espeically if you're a hearing person.