Google launched a deeper integration with Twitter – a new Twitter box.
I decided to tweet a few times and see if I could get my own Twitter box.
Guess – what, I could – and you can too!
Matching the twitter name to your searched name seems to help.
Also make sure to tweet several times.
See for example:
Update: It also helps to define your official Twitter page using schema.org markup, Wikidata and claiming your knowledge panel. This is especially important if you share a name with others who tweet regularly.