You look different. Have you had your hair styled differently?
Yes, I have had my hair styled differently.
Remember that question marks do not exist in speech. Interrogatives are marked in both speech and writing by inversion of indicative word order.
This use of "have" is admittedly a bit odd, but essentially regular.
I shall/will have X do Y
expresses my commitment or intention to do in the future what is necessary to cause X to do Y in the future, but
I have had X do Y
expresses that I have already done what was necessary to cause X to do Y. Notice the past aspect of the present tense.
These forms are made interrogative in the standard ways
You have had X do Y
becomes an interrogative by
Have you had X do Y
Did you have X do Y
This use of "have" can be made passive as follows
I have had Y done
I have had Y done by X.
And these passives can be made interrogative passives as
Have you had Y done