Is it arrogant in writing to explicitly say I came up with the term?
Fear of appearing arrogant made me think to just say:
X will be used throughout the thesis to refer to the concept of Y
without informing that no one has used it before.
What do you think? Any alternatives to introduce newly coined terms by yourself?
No, it’s not arrogant to make a definition and to claim it. Because making a definition is not to your credit — it’s not a discovery. Anyone can make up definitions. They are made for convenience, and the only test of their merit is whether they do actually turn out to be convenient. For that, you have to go on to use the definition you made to say something of substance. A definition is only a preliminary step.