"oon" can stand for "olen" in spoken Finnish. The sentence decides its meaning.
Moi! Mä oon Anna. - Hi! I'm Anna.
oon here: am - spoken form of 'olen'
Written Finnish: Hei! Minä olen Anna.
Mä oon kipee. - I'm sick.
oon here: am - spoken 'olen'
Written Finnish: Minä olen kipeä.
Mä oon käyny Tallinnas kerran. - I've been to Tallinn once.
oon here: have - spoken 'olen'
Written Finnish: Minä olen käynyt Tallinnassa kerran.
Mä oon aina halunnu oppii suomee. - I've always wanted to learn Finnish.
oon here: have - spoken 'olen'
Written Finnish: Minä olen aina halunnut oppia suomea.
Mä oon just lähdössä. - I'm just about to leave.
oon here: am - spoken 'olen'
Written Finnish: Minä olen juuri lähdössä.
Mä oon tosi pahoillani sun puolesta. - I'm really sorry for you.
oon here: am - spoken 'olen'
Written Finnish: Minä olen tosi pahoillani sinun puolestasi.
Spoken and written Finnish are different registers. The examples show how "oon" is used here and pair it with the written sentence. Learn the meaning in context rather than replacing every occurrence of a word.