Ramban in his commentary to that verse offers three explanations:
Lavan was referred to by his paternal grandfather Nachor's name because Nachor held a higher status than Lavan's father Bethuel, as seen later in the agreement made between Yaakov and Lavan, "the G-d of Avraham and the G-d of Nachor" (Bereishis 31, 53). This practice was despite Lavan being the son of Bethuel (Bereishis 28, 5), emphasizing Nachor's prominent role in their family (Bereishis 22, 22).
Additionally, this may be because Bethuel had a tarnished reputation, leading Lavan to prefer associating his lineage exclusively with his paternal grandfather. This is suggested by the order of mention in an earlier verse "Lavan and Bethuel answered" (Bereishis 24, 50), where Lavan precedes his father, indicating Bethuel's diminished significance.
Yaakov's choice of reference could also be a mark of respect to Avraham, as it linked the entire family's lineage to Nachor, Avraham's brother (Bereishis 22, 23), thereby emphasizing their connection to the illustrious Avraham.