Edit (by @dk14 as suggested by moderators and comments)
WARNING: If you use credential.helper store from the answer, your password is going to be stored completely unencrypted (“as is”) at ~/.git-credentials. Please consult the comments section below or the answers from the “Linked” section, especially if your employer has zero tolerance for security issues.
Even though accepted, it doesn’t answer the actual OP’s question about omitting a username only (not password). For the readers with that exact problem @grawity’s answer might come in handy.
Original answer (by @Alexander Zhu):
You can store your credentials using the following command
$ git config credential.helper store
$ git push http://example.com/repo.git
Username: <type your username>
Password: <type your password>
Also I suggest you to read
$ git help credentials