changing the username part of my gmail address

if what bugs you is the name people see when you email them, not the address itself, that you can change any time. Google Account > Personal info > Name. takes effect on new emails straight away.

for years the answer was flat no for @gmail.com addresses. Google has started rolling out a change option though, under Google Account > Personal info > Email > Google Account email. if it lets you edit it there, your old address sticks around as an alias so mail to it still arrives. if there's no edit option, it hasn't reached your account. fallback is a new account and forwarding the old one into it.