To Tell The Truth
Could "My name is --" be a reference to the game show To Tell The Truth? I have no evidence to support this other than the fact that the show was airing in syndication in 1970 when the letter was written, and each segment was introduced by three people saying "My name is..."
Here's an example:
To Tell The Truth - The Doodle Book
Here's an example:
To Tell The Truth - The Doodle Book