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Does people started call him Buddha ?
It's according to the suttas that he told people to remember him as "Buddha". For example, at the end of the Dona Sutta (AN 4.36):
Remember me, brahman, as 'awakened.'
... and so, brahman, I'm awake.
Alternatively the Dharmafarer translation of this sutta:
Therefore, brahmin, remember me as the Buddha.”
... therefore, brahmin, am I buddha.
The Pali for that last line:
tasmā buddho’smi brāhmaṇâ ti
"Buddha" isn't the only word used; for example there's also tathagata.
Upvote:5
Definition of Buddha based on Pali Dictionary is here:
Buddha Skt., Pali, lit., “awakened one.”
The Wikipedia entry is here:
The word Buddha means "awakened one" or "the enlightened one".
Hypothetical root budh "perceive" 1. Pali buddha – "understood, enlightened", masculine "the Buddha"; Aśokan (the language of the Inscriptions of Aśoka) Budhe nominative singular; Prakrit buddha – ‘ known, awakened ’; Waigalī būdāī, "truth"; Bashkarīk budh "he heard"; Tōrwālī būdo preterite of bū, "to see, know" from bṓdhati; Phalūṛa búddo preterite of buǰǰ , "to understand" from búdhyatē; Shina Gilgitī dialect budo, "awake"; Gurēsī dialect budyōnṷ intransitive "to wake"; Kashmiri bọ̆du, "quick of understanding (especially of a child)"; Sindhī ḇudho, past participle (passive) of ḇujhaṇu, "to understand" from búdhyatē, West Pahāṛī buddhā, preterite of bujṇā, "to know"; Sinhalese buj (j written for d), budu, bud, but, "the Buddha".
Buddha means one who understood or awakened. This understanding / awakening is based on intelligence gained.