More than just weird - it's actually wrong. The correct construction is 'Thank you for + gerund'. For negative sentences, the 'not' goes before the gerund : 'Thank you for not xxx ing'. Take note of correct forms when you see them, learn them and use them. That's all you need to do.

You COULD say "I would thank you not to forget my name" as in making a request of someone but frankly it sounds a littl ominous and kind of rude.....but really that's the only way that would grammatically make sense.

Thank you for not forgetting my name.