Can I just fill Name, Email, Home Page at the end of /questions/ask page?
This isn't possible any more.
"You must be logged in to ask a question on Stack Overflow"
You'll need to create an account. The larger sites on Stack Exchange do not allow guests to post questions. There's more background on this decision and a list of the sites in this answer:
You can click on your name on the top of the site to get to your profile. There, click edit and change the name to whatever you want. You can only do this once every 30 days!. The name you set here will automatically be displayed on all your questions and answers, including those posted before.
If you want to post questions/answers under a different name for whatever reason, you have to create another account.