A provider joins TER and chooses her handle just like any member does.

Now if she gets her first review (Whether she has joined TER or not.), she gets a profile with the handle she uses professionally, according to the TER member who has written the review.

I think that is what you are refering to.

Is it true that for a provider to have a handle in the TER the client has to write a review about them?

...uses in her website or ad.  If she subsequently uses another name her profile may say "Gertrude/Gladys."

However, a provider can choose a different name for her posting handle and also have another handle as an alias.  Confused yet?