"Now" or "Today", which one sounds better for a company title?

If it’s Shakespeare I’d go with Shakespeare On The Morrow: Hither Thither And Yon.

Otherwise Now.

Why not “post-haste”?

If you combine them, you get Noway. ;-)

@Brian1946 Noway, I’ll not do it.

It really depends on what you are trying to communicate.

If you are trying to say the company is up to date and modern, use “Today”.

If you are trying to communicate prompt and efficient service, use “Now”.

I’ll choose “Now.”

It doesn’t matter. It’s a name. You’d choose the one you like the sound of.