Just for entertainment purposes, let me pull out my Japanese-English dictionary and see what the names we're choosing mean.
Hori
This one is simple. Either "moat" or "dig." It also has the advantage of actually being a name, but it's typically a family name rather than a first name.
Morikano Hayato
This one's also fairly easy. Hayato is a real place. Using a place name as a family name is fairly common. Implication is simply that you're a member of or a descendant of the family that founded the city.
As for Morikano...could be interpreted a few ways, with "forest power" and "harvested forest" being likely candidates.
Shizume Ninokara
Best guess for Shizume is "quiet eyes." Though I wonder if you really intended shizuNE, which is a fictional name used by various female characters in anime, and is probably a derivative of the same root meaning quiet/calm/serene/etc.
Ninokara is a bit troublesome, but "the husk/shell of two" isn't unreasonable
Metasan Ketusune (His real name)
Metasan? "San" is an honorific. It's basically like "Mr." And "Meta" is the Japanese loanword for the unit of measurement: "meter." So your name is "Mr. Meter."
Which makes one wonder what we call you when we're being polite. Shall we call you Metasan san? Or is your real name simply Meta, but you're a condescending bastard and you refer to yourself with an honorific? Which would be like someone introducing themselves to you by saying, "Hi. My name's Mr. Meter. You can call me Mr. Meter. Don't forget the Mr."
Ketusune is problematic because there is no "tu" character in japanese. Closest approximations would be Ketsusune or Ketsune, both of which are also problematic. First interpretation of "Ketsune" I see is "Ass, huh?" As in, vulgar ass. Not donkeys. If we stretch the grammar a bit we might be able to interpret as the impolite command for of "pinch hair" but I'm a bit rusty on the exact meanings of using unconjugated verb roots in japanese. On the other hand, Ketsusune rather than Ketsune...best I get there is "Ass shin." I'm not exactly sure what an ass shin is.
However...just a guess, it's possible this wasn't a word you made up, but rather, you
heard somewhere, in which case you probably intended
kitsune, which means fox.
But, given the choice of including the honorific as part of your name and specifying that it's the "real" name..."Mr. Meter Ass, isn't it?" might be reasonable.