Should we tell our 9 year old she is 'autisitic'

We are looking for advice about our 9-year-old daughter who has just been given ASD (high functioning) and ADHD diagnoses. The issue we are wondering about is the CAMHS advice that we should tell her these labels apply to her.

I think future support through an EHCP/statement (which she does not yet have) may depend on her being told and that this is justified because naming the problem helps you to face it.

We’re struggling with the potential stigma (from self as much as from others) it could bring for someone who is already low in confidence.

We are clear that the ADHD is an issue (she has very strong hyper-focus, poor ability to plan or stay with a task, etc) and find that less sensitive. The ASD is less clear to us because shyness often seems an equally good explanation (eg for poor eye contact) and because she is intensely social (begs for playdates, usually generous and warm with friends despite preferring to talk than listen). 

Any advice/experiences welcomed with thanks.