Twitter and Search Engine Deletion?

[Addison]

So I recently changed my twitter @ name and twitter display name and I made it a private account. (I realized how much I do not want my full name on the internet anymore and would much rather use a fake name.)
I've been clearing things from google as much as i can, however, there are still links from when my full name was on my account and it was unprotected. (It links automatically to my new @ name because it's technically still the same account)
I was wondering if anyone knows about how long it will take google to update that information so that when you search my real name, my twitter will not show up at all. Or if there is any way I can delete everything so I don't have to just delete the tweets individually. I figured making my account private would hide my old tweets as well, but I guess I was wrong?
I tried to contact Twitter, but it's been a month and no response.
Thank you!

[Marvin]

It takes time for Google bots to crawl and index your Twitter account.