I don't have the slightest idea.

[goten]

Hello.

A: Who is that woman Terry is talking to?
B: I don't have the slightest idea.

"I don't have the slightest idea."
Is this commonly used?

[peppy_man]

Yes, it is often used.
"Don't have the slightest idea" means that you have no idea about something at all. In this case, you have no idea at all about the woman Terry is talking to.
You can also say ''I haven't the slightest idea.

[rewboss]

Other possible idioms:

I haven't the foggiest (idea)
I haven't/don't have a clue
Your guess is as good as mine

[peppy_man]

Another possible idiom.
'I haven't the vaguest idea.'
Hope this would help.