In the Pali commentaries, there is a contradiction regarding the name of Thera Anuruddha's father. Somewhere he is said to be the son of Sukkodana, and somewhere of Amitodana. Both Sukkodana and Amitodana were Suddhodana's brother. So, in any case, Anuruddha was surely a cousin of the future Buddha. But his relation with Thera Ananda becomes controversial. Everywhere Ananda is said to be the son of Amitodana. So he might be either a cousin or a brother of Anuruddha. Most modern Western scholars seem to prefer the latter alternative albeit insisting that they were probably step-brothers from different mothers "as the texts do not refer to the two as brothers and imply that they grew up in different households." If that is the case, why not accept Anuruddha as the son of Sukkodana? Are there more weightage in the claim of Amitodana? Can someone answer with commentarial references?
According to the Apadana Atthakatha, Anuruddha was the youngest brother of Mahanama, and their father was the paternal uncle of the Buddha. It doesn't mention the father's name.
It is undisputed that Anuruddha was Mahanama's own brother, from various sources, including the Vinaya in Pli Tv Bu Vb Pc 6.
According to this page:
Mahānāma. A Sākiyan rājā, son of Amitodana; he was elder brother of Anuruddha and cousin of the Buddha. When the Sākiyan families of Kapilavatthu sent their representatives to join the Order of their distinguished kinsman, Mahānāma allowed Anuruddha to leave the household, he knowing nothing of household affairs. Vin.ii.180f.; DhA.i.133; iv.124, etc.; but according to Northern sources (Rockhill, p. 13) he was son of Dronodana; according to ThagA. (ii.123) Ananda was a brother (or, at least, a step brother) of Mahānāma, for there Ananda's father is given as Amitodana. But see MA.i.289, where Mahānāma's father is called Sukkodana and Ananda's Amitodana.
From the abbreviation list of this journal edition, ThagA is the Theragatha Atthakatha and MA is the Majjhima Nikaya Atthakatha.
According to this page which quotes a book called "Relatives and Disciples of the Buddha" by Radhika Abeysekera:
Anuruddha was one of Prince Siddhattha’s cousins. His father, who was named Amitodana, was a younger brother of King Suddhodana. Amitodana had two consorts. Anuruddha, his brother, Mahanama and his sister, Rohini, were born from one consort. Ananda, who later became the Buddha’s personal attendant, was the son of the other consort. As such Ananda was Anuruddha’s step-brother.