He was baptised Theophrastus von Hohenheim, near Einsiedeln in Switzerland, in 1493 or 1494, the year is genuinely unresolved. The familiar four-part name is a composite he never used: Aureolus is contemporary but attaches to him late, and Philippus is posthumous, appearing first on his tombstone. The by-name Paracelsus shows up around 1529 and may not be his own coinage; it is read either as a claim to surpass the Roman medical writer Celsus or as a Latin play on Hohenheim, celsus meaning high.
The claim that the English word bombastic derives from his family name Bombast is false, and it is repeated constantly, including in otherwise careful books. Bombast is cotton wadding, the padding in a doublet, from Old French bombace and ultimately Greek bombyx, and it acquires the figurative sense of inflated language in the 1580s, decades after his death. Bombast was a genuine name in his father's family, which is why the story is plausible enough to survive. It is a coincidence.
The habits behind the legend are real enough. He lectured in German rather than Latin, which was close to scandalous, and at Basel in 1527 he publicly burned the books of Avicenna and Galen, announcing that his own experience was worth more than a thousand years of authority. He was run out of Basel within the year and spent most of his life travelling and quarrelling.