The Romans are primarily responsible for all of our names for the days of the week. Romans reckoned their Monday through Sunday schedule as Dies Lunae (day of the moon), Dies Martis (Mars), Dies Mercurii (Mercury), Dies Jovis (Jupiter), Dies Veneris (Venus), Dies Saturni (Saturn), and Dies Solis (sun).
As the Romans worked very, very hard to conquer all of the known world, knowledge of the Roman week spread throughout their various colonies and was adopted by other cultures, who plonked their own gods and goddesses in for what they saw as their Roman equivalents. The Norse and Anglo-Saxons, in particular, were fond of the approach. Mars was Tiu, Mercury was Wodin, Jovis was Thor, and Venus was Frigg (not, as is sometimes believed, Freya, who was more of a minor Teutonic goddess).
In the case of Dies Lunae and Dies Solis, well, the Germans/Norsemen/Saxons/etc. pretty much left them alone for reasons that aren’t entirely known. My favorite reason for Dies Solis retaining its Roman distinction amongst the Saxons is that, as a culture from a considerably cloudier and darker place than, say, Italy, the sun just didn’t figure that prominently into their mythologies.
So who’s the guy in the hat already?
The Roman Dies Solis was declared “venerable day of the Sun” by Emperor Constantine on March 7, CE 321, seriously, you can look it up, although it’s pretty boring. Comforting to know that governmental regulations haven’t changed that much in the past 1500 years. This was in honor of Mithras, primary god of the Roman mystery religion, Mithraism, who was also known as Sol Invictus (the unconquered sun). That’s him in the hat.
And why the hat?
Even the unconquered sun likes to dress snappy from time to time.