_Se_ is a pronoun. It is used as direct and indirect object designating the same person or thing as the subject in verbs at the third person. To designate something else, use _le_, _la_, _les_, the speaker use _me_, _nous_ and the person(s) to whom one speaks, use _te_, _vous_.

Then there is the class of _pronominal verbs_ for which the use of a reflexive pronoun (_se_ at the third person, _me_, _nous_ at the first, _te_, _vous_ at the second) changes the meaning and for which the function of the reflexive pronoun is not well defined.  Trying to analyze them is doomed for the same kind of partial success as trying to analyze phrasal verbs in English by separating the verb and the preposition.

In _il se lave_ we are clearly in the first situation.

In _Paul se dit..._, we are perhaps in a case where a verb is becoming pronominal, you better analyze that as _Paul dit à lui-même..._, but it is acquiring a slightly different meaning (and different from the impersonal use of _il se dit_).

In _il s'appelle Paul_, the verb has become pronominal in this use (_he is named Paul_ is a better translation than _he calls himself Paul_) but you can somewhat get the meaning from a simple analysis.

In _il s'ennuye_, the meaning is clearly different (_he is bored_, not _he is annoying himself_).