Without any context, the obverse of gold bar money appears to be a series of incoherent swoops and lines. Elegant, but not meaningful. However, this little-discussed design was actually quite important in the acceptance of gold coins among the populace.
Most sources limit their discussion of it to the simple description, "Mitsutsugu and his signature." Before we look at the significance of this, let's take a look at those two elements.
It took me quite awhile to figure out how the top characters on gold coinage created the name Mitsutsugu - "光次" in Japanese. Perhaps this is obvious to native Japanese speakers, but as a native English speaker, it was not. After becoming very familiar with both the coins and the characters themselves, I was able to see the correlation. The illustration below shows how they relate
The bottom portion is referred to as Mitsutsugu's signature. His full name was Goto Mitsutsugu, and I began looking at this more closely in an attempt to figure out what part of his name it represented - "Mitsutsugu," "Goto," or both. This was relevant to a thread of research related to a different piece that isn't important for our current discussion.
The shape didn't clearly correlate to any of the Japanese characters in his name. As it turns out, this section is referred to in Japanese sources as "武家風花押," which translates to "Samurai-style signature." However, cultural context is lost in this translation. The last two characters, "花押," become "signature" in English, but are originally "kao."
A kao is a form of Japanese signature, but it is not a stylized version of one's name like we think of as a signature in Western culture. A kao is more of a personal seal; a stylization of a character(s) that may or may not have any relation to one's name, and something that can be passed down through a family. The history and origin of a kao can be so complex that entire books have been written on the individual kao of important rulers.
Therefore, it's unclear if this kao is specific to Mitsutsugu, or if it was passed down through the Goto family. I suspect the latter, but have nothing beyond inference to back that up.
The question now becomes: why put one man's name on all of their gold coinage? Americans got upset when Victor David Brenner put his initials too prominently on the reverse of the wheat penny, but here's a coin where half of the entire design is dedicated to one man's name for over 200 years.
Again, the explanation lies in cultural differences. One's personal honor was (and is) extremely important in Japan. This is a society where it was better to die than to lose your honor. By putting his name on the coins, Goto Mitsutsugu affixed his entire family's honor to these pieces, stating that they were legitimate and trustworthy. Other prominent families would have recognized this and been more likely to trust them, knowing who they were backed by. Without a name attached, who could have said who made them? Whose honor would have been at stake had they been faulty?