You can sing 'The Name Game' with (almost) every name.
Sometimes it sounds better if you use a shorter nickname. (e.g. Mary for Marylin)
Unless your name begins with a vowel (A, E, I, O, U), 'B', 'F' or 'M' you don't have to care about special rules.
The verse for the name 'Gary' would be like this:
Gary, Gary, bo-bary
At the end of every line, the name gets repeated without the first letter: Gary becomes ary
If we take (X) as the full name (Gary) and (Y) as the name without the first letter (ary) the verse would look like this:
(X), (X), bo-b(Y)
If you have a vowel as the first letter of your name (e.g. Earl) you do not truncate the name.
The verse looks like this:
Earl, Earl, bo-bearl
In case of a 'B', an 'F' or an 'M' (e.g. Billy, Felix, Mary) there is a special rule.
The line which would 'rebuild' the name (e.g. bo-billy) is sang without the first letter of the name.
The verse for the name Billy looks like this:
Billy, Billy, bo-illy
For the name 'Felix', this would be right:
Felix, Felix, bo-belix