I am just a contributor on Byteball. There is no way to "download" the wallet under your Steemit name. You just download it and install it and that's it.

If you mean that you named your device or wallet as some other name, then these you can change anytime:

• Home > Gear icon -> Wallet alias
• Burger menu > Settings > Device name

But these names doesn't matter much, what is important is the Steem attestation with chatbot.

If you mean by "downloading under the name" as you already made a Steem attestation with other Steemit user then you need to do the clean install.