The HaKsav VeHakabbalah makes this observation. He writes there:
לבן אחי אמו. הזכיר הכתוב כמה פעמים אחי אמו להודיע כי כל מה שהשתדל יעקב בצאן לבן להשקותם ומה שהיה חומל על רחל לא עשה לכבוד לבן (או לפי שהיה לו בראייתה התעוררת לאהבתה) רק לכבוד אמו, בשביל שהיה אחי אמו, שבכל אותן הדברים הזכיר בלבו את אמו שנתנה לו העצה ללכת אל לבן, (רב"ח)
Lavan the brother of his mother: The verse writes several times that he was “the brother of his mother” to make known that all that all the effort that Yaakov expended with the white flock to water them, and that which was merciful to Rochel, he did not do out of honour to Lavan but rather to honour his mother, since he (Lavan) was the brother of his mother, that in all those things he remembered in his heart his mother who had given him the advice to go to Lavan.
So it was to emphasise the fact that throughout he was acting out of sincere love and honour to his mother, following her advice the whole time.
Alternatively the Paneach Raza wants to suggest that each mentioning had a specific reason. In the first instance upon seeing Rochel, he remembered that whilst she was the daughter of Lavan, Lavan was the brother of his mother, to allay his fears about marrying Rochel, in that in the same way his mother did not learn from the evil actions of her family, the same would be true of Rochel. The second time of saying this was with regards to the flock of sheep he saw. It was then that he realised that he might have to claim them by force, and could be rest assured that he would have Divine assistance by virtue of the fact that despite Lavan being an evil man, he was his mother's brother and thus could rely on his mother's merits. The final time it makes reference to Lavan as his uncle, was when he gave the flock to drink. And it was precisely because Lavan was his mother's brother that he immediately gave his heart to them for grazing and watering and guarding them from plunder from other fields.
The Rabbeinu Bachaye first answers similar to the HaKsav VeHakabbalah but also provides another answer. He writes there:
There is yet another reason for the repeated mention of the words אחי אמו, brother of his mother.” Whenever a person hears or sees an object he desires, he is suddenly capable of performing tasks which he cannot perform in order to secure something which his heart does not covet. The reader of this passage could be forgiven if he had thought that seeing Yaakov was taken with Rachel’s beauty he desired her physically and this is what gave him the strength to move the rock single-handedly. The Torah refers time and again to the fact that Lavan was the brother of Yaakov’s mother in order to make us aware that physical passion had nothing to do with Yaakov’s sudden burst of strength in moving the rock. The Torah was so concerned not to create the impression that Yaakov’s sudden burst of strength was inspired by passion that instead of writing: “as soon as Yaakov set eyes on Rachel he rolled the rock, etc.,” the Torah wrote instead (in a somewhat clumsy style) “it was when Yaakov saw Rachel the daughter of Lavan, the brother of his mother, and the flock of Lavan the brother of his mother, Yaakov approached and rolled the rock etc.” (Sefaria translation)