Ἀλφαῖος

Matthew 10:3 Ἁλφαίου of Alphaeus

Philip and Bartholomew; Thomas and Matthew the tax collector; James son of Alphaeus, and Thaddaeus;

Here: Probably from the Aramaic name Ḥalfai. It tells this James apart from James son of Zebedee (10:2). Mark 2:14 also calls Levi "son of Alphaeus," but whether it is the same Alphaeus is unknown.

Mark 2:14 Ἁλφαίου of Alphaeus

As He was walking along, He saw Levi son of Alphaeus sitting at the tax booth. “Follow Me,” He told him, and Levi got up and followed Him.

Here: The father's name, a Greek form of an Aramaic name (probably Ḥalphai). It identifies Levi in the usual Jewish way, by his father. Mark 3:18 also has a 'James son of Alphaeus', which raises the question of whether they were brothers.

Mark 3:18 Ἁλφαίου of Alphaeus

Andrew, Philip, Bartholomew, Matthew, Thomas, James son of Alphaeus, Thaddaeus, Simon the Zealot,

Here: Probably the Aramaic name Ḥalfai. Levi is also called 'son of Alphaeus' (2:14). Whether it is the same Alphaeus is unknown. It was not a rare name.

Luke 6:15 Ἁλφαίου of Alphaeus

Matthew and Thomas; James son of Alphaeus and Simon called the Zealot;

Here: A Greek form of an Aramaic name, probably Ḥalpai. The bare genitive ('of Alphaeus') is the normal Greek way to say 'son of'. 'Son' is understood, not written.

Acts 1:13 Ἁλφαίου of Alphaeus

When they arrived, they went to the upper room where they were staying: Peter and John, James and Andrew, Philip and Thomas, Bartholomew and Matthew, James son of Alphaeus, Simon the Zealot, and Judas son of James.

Here: A bare genitive, 'of Alphaeus', which in a name normally means 'son of'. Levi (Matthew) is also called 'son of Alphaeus' (Mark 2:14). Whether these are the same Alphaeus is unknown.