i dont know how many people were told that by R, Chaim shlita, or how it was said. But i do know two of the shiras who changed their names. Neither went to R Chaim saying ,”Hi, can I keep my name?”. They went for brachos and his response, from what i remember, was that Shira is not a name. My understanding was that we don’t really know if the need to change the name was somehow connected to the bracha he was giving them or the desire for one. Perhaps if they weren’t in need of certain things in their lives, they would not have needed to change their names.
I don’t mean that he made up the reason, ch”v, i just mean that it may not always apply.
I myself have never asked.