Mi chiamo is used to translate My name is or, more literally, I am called. The literal translation would be "I call myself".
The particle "si" can be attached to the end of many verbs to make them reflexive verbs. Thus:
Chiamare. To call.
Io chiamo il mio gatto. I call my cat.
Mi chiamo Ettore. My name is (I call myself) Ettore.
You can also say: Il mio nome è Ettore (literally, My name is Ettore), although it's less common.
In ti amo, the verb is not reflexive:
Ti amo. I love you.
Amo comes from amare, to love. This is the infinitive verb, and if you attach "si" to it, it becomes amarsi, the reflexive variant "to love oneself". You'll then have...
Io mi amo. I love myself.
Lui si ama. He loves himself.
Loro si amano. They love themselves.
And so forth.
To say I like myself, however, you would say Mi piaccio, not Mi piace. When used in its reflexive variant, the verb must be conjugated according to the subject.
Mi piaccio. I like myself. ("A me piaccio")
Mi piace. I like (it). ("A me piace")
Another example verb can be fare male (to hurt):
Mi faccio male alla gamba. I hurt my leg. ("I hurt hurt myself at the leg")
Mi fa male la gamba. My leg hurts.
The reflexive verb changes depending on the subject in the first sentence:
Io mi faccio male, tu ti fai male, lui/lei si fa male, noi ci facciamo male, voi vi fate male, loro si fanno male. I hurt myself, you hurt yourself, he hurts himself, etc.
The verb in the second sentence doesn't change, however, because it is not a reflexive verb. We could translate the sentence roughly as "To me hurts the leg". Notice that the subject pronoun is not used.
Mi fa male, ti fa male, gli/le fa male, ci fa male, vi fa male, a loro (gli) fa male.
It hurts me, it hurts you, it hurts him, etc.
Hope this helps!