Jesus was REGARDED as the son of Joseph

[TonyChanYT]

Berean Study Bible Luke 3:

23 Jesus Himself was about thirty years old when He began His ministry. He was regarded as the son of Joseph, the son of Heli,

known, supposed
ἐνομίζετο (enomizeto)
Verb - Imperfect Indicative Middle or Passive - 3rd Person Singular
Strong's Greek 3543: From nomos; properly, to do by law, i.e. To accustom; by extension, to deem or regard.

Strong's Concordance:

to practice, consider
Usage: I practice, hold by custom; I deem, think, consider, suppose.

Thayer's Greek Lexicon:

1. to hold by custom or usage, own as a custom or usage; to follow custom or usage; passive νομίζεται it is the custom, it is the received usage: οὗ ἐνομίζετο προσευχή εἶναι, where according to custom was a place of prayer
2. to deem, think, suppose: … as was accustomed to be supposed

Luke used this Greek word to hint that Joseph was not the biological father but a legal one.

Barnes:

As was supposed - As was commonly thought, or perhaps being legally reckoned as his son.

I don't think Joseph went through the formal legal proceedings to adopt Jesus. Nonetheless, Joseph considered Jesus his own son, having all the legal inheritance rights when Joseph died.