As far as I can tell, this is just a coincidence. This producer wasn't part of the original School Days visual novel production team, and he worked on anime before the School Days anime or VN (the earliest apparently being Meine Liebe (2004)). The School Days VN came out in 2005, which seems to rule out it being a pen name chosen because of the character. He made a brief joke on the 39th episode of the radio show "Radio School Days" regarding their names which seems to confirm that they aren't related.
According to School Days Wiki, the basis for (the fictional character) Makoto's name is actually from Itou Hirobumi, who was prime minister of the Japanese empire for four terms.
As a note, Itou Makoto (written as 伊藤 誠) isn't an uncommon name. Itou is the 6th most common surname, and Makoto is the 18th most common given name (these figures may change somewhat depending on the source, time period, etc. but are just meant as demonstrations of commonality). This Wikipedia disambiguation page lists 6 real people with that name. While it's still a pretty big coincidence that a producer would end up having the same name as a character, it's not unbelievable.
Source (for everything unsourced above): jp.wikipedia article