Not to deny that Shakespeare had some importance in immortalizing Julius Caesar, but the Bible was also probably heavily influential.

"Render unto Caesar the things that are Caesar's, and unto God the things that are God's"

The Bible makes several references to "Caesar" (meaning any Roman Emperor, not just Julius Caesar). The Bible does not mention Sulla and Marius.

Since the Bible was probably the most influential book in Western civilization, its use of the word "Caesar" probably popularized that title (and therefore, Julius Caesar as the originator of that title) throughout Europe, and not just in England or English speaking countries.

I would say Shakespeare.

"Et tu Brutus" is something everyone knows but cant actually be attributed to Caesar, but it was immortalized in Shakespeare's plays. Much like how Romeo and Juliet are household names but the stories they originally came from are not.