In Mahabharata, why are Arjuna and his brothers called Pandavas and Duryodhana and his brothers called Kauravas?
Is there any reason to call them like that?
Kuru was an ancient lunar dynasty king of Hastinapura and an ancestor of Shantanu. The patronymic (i.e. last name form) of the name Kuru is Kaurava, so in a broad sense you could say that everyone descended from Kuru is a Kaurava, which includes both the sons of Pandu and the sons of Dhritarashtra. But the way Vedic patronymics worked was as follows: if X is the eldest son of man Y, then the sons of X adopt the same patronymic that Y had. But if X is a younger son of man Y, the sons of X just use X's name to form a patroymic. (Except when Y's elder sons have no children, in which case X's sons constitute the senior branch of the family.) Shantanu was called Shantanu Kaurava, his sons were called Vichitravirya Kaurava and Chitrangada Kaurava, and Vichitravirya's two sons were called Dhritarashtra Kaurava and Pandu Kaurava.
Now Dhritarashtra's sons would be called Duryodhana Kaurava and the like, but the sons of Pandu, being the sons of a younger son, would adopt Pandu's name as their patroynmic. So they would be referred to as Yudhishtra Pandava, Bhima Pandava, etc. That is why the sons of Dhritarashtra are Kauravas and the sons of Pandu are Pandavas.
On a side note, it should be noted that all this stuff about ancestry and descent is not necessarily about actual biological relations. For instance Dhritarashtra and Pandu are actually the biological sons of Vyasa, not Vichitravirya, as I discuss in this answer. And the Pandavas are the biological sons of the gods Yama, Vayu, Indra, and the Ashwini Kumaras, not Pandu. But they're still considered these people's adopted sons, as per the practice of Niyoga.
Historically Kauravas and Paandavas both belong to the "Kuru" dynasty. For example, Duryodhana + brothers are "Kauravas". While Yudhishtira + brothers are "Kauravas" as well as "Paandavas".
In Chapter 10, Krishna himself says that:
Verse-19 "O Best among the Kurus (Arjuna), I shall relate to you about my divine manifestations which are prominently conspicuous, for there is no end to my expansion."
Verse-37 "I am Vasudeva among the Vishnus (they are a branch of Yadava-clan to which Krishna belonged), I am Arjuna among Pandavas, I am Vyasa among the sages and also among poets I am Ushra (also called Shukracharya "The teacher of the demons" (Rakshasas)."
From queen Satyavati's blood line ("biological kids" point of view), Duryodhana + brothers were actually Kauravas. But Yudhishtir + brothers + Karna were neither Kauravas nor Paandavas, as they were born out of a boon given to Kunti.
I believe the term Kaurava and Paandava would have been used during or sometime before the Mahaabhaarata war had begun to merely distinguish between the cousins.