Why is the Monokuma's eye in the school crest?

Question

Hope's Peak Academy's crest looks like this:

In the center is a fountain pen and what looks to be a Monokuma's eye:

But the school was established before Monokumas were created if I'm not mistaken.

Before any of the games take place, Hope's Peak was a small-scale facility that survived on a government subsidiary and graduate donations. However, the research was often blocked by a lack of resources. The school's steering committee was not satisfied with this, so they instituted the preparatory school system in order to bring in more money. (Ref)

Why then is the Monokuma's eye in the logo? Or were the Monokuma designed to have the eye because of the logo?

Answer 1

From the Wikia:

Prior to the series, this cunning and vile being is actually a model animatronic bear used as an avatar to interact with the students by the mastermind. There are seemingly infinite copies of Monokuma, and he seems to also have the ability to teleport everywhere within the academy compounds.

^{(Emphasis mine)}

Prior to The Tragedy:

Monokuma was apparently designed by the Towa Group's robotics division, under the supervision of Monaca Towa. She claimed that she wanted to develop a series of robots that could assist in rescue operations and other scenarios that would be dangerous for humans - in reality, she wanted to build an army for Junko Enoshima's plans. The Monokuma units were then secretly distributed to the various branches of Ultimate Despair, with Junko taking several for her plot at Hope's Peak Academy.

^{(Emphasis mine)}

It can only be assumed that the eye was shaped after the Hope Peak Academy's crest because it was supposed to be a part of the school's rescue operations. At least this much is evident that the Monokuma's eye is modeled after the school's crest and not the other way round.

Answer 2

The Monokuma's eye was created by

Junko the Ultimate Despair. She designed the bear and help the hero kids with their plan.

I do not know what the crest originally meant, but I do know it didn't mean despair from Monokuma.

Answer 3

It is possible that the crest was changed, but I see this as unlikely. I think that Monica and Junko wanted Monokuma to be inspired by the design of the crest (it is also possible that Kazuichi was the one who built Monokuma, when he was ultimate despair, as he is seen in Danganronpa 3: The End of Hope's Peak High School making a giant one, and has been confirmed to have made all the ones in UDG).

I think Monokuma's design was inspired by the school crest, the half light half dark is seen in the crest, and is incorporated into Monokuma's design. The eye from the crest was made to bring despair and unease to anyone who encountered a Monokuma. That's what I think anyway.