Yes, the "s or se" like in s'appeler, s'exclamer, se détendre etc is conjugates according to The subject.
t's The pronominal form of "appeler"
you call yourself Paul
the "s'" before "appeler" indicates that the subject and the object of the verb are identical.
he calls himself ...name
son / sa appelle = s'appelle
he calls himself / she calls herself
You call yourselves
reflexive verb appelle
il s'appelle
The "sa" form of the possessive adjective "son" which means "his/her"
It's tempting to try to 'agree' these with the gender of the owner but only the first letter is determined by the owner (m = my; t = your, s = his/her) etc. The rest of the adjective is related to the gender and number of the thing they own
On s'appelle Julian and Julie
On s'appelle Marie et Pierre.
Nous nous appelons Marie et Pierre.
Vous vous appelez Ethan, Benji, and Simon.
Our names are Tom and Jerry
s'appelle
s'appelle
We call you Fred
Appelez une ambulance! (Call an ambulance!)