All 3 Uses

assume
in
The Picture of Dorian Gray - 20 chapter version
(Edited)

But now and then a complex personality took the place and assumed the office of art; was indeed, in its way, a real work of art, Life having its elaborate masterpieces, just as poetry has, or sculpture, or painting.
Chpt 4

assumed = took on or adopted
There were moments, indeed, at night, when, lying sleepless in his own delicately-scented chamber, or in the sordid room of the little ill-famed tavern near the Docks, which, under an assumed name, and in disguise, it was his habit to frequent, he would think of the ruin he had brought upon his soul, with a pity that was all the more poignant because it was purely selfish.
Chpt 11 *

assumed = false (taken on or adopted)
...Pietro Barbi, the Venetian, known as Paul the Second, who sought in his vanity to assume the title of Formosus, and whose tiara, valued at two hundred thousand florins, was bought at the price of a terrible sin;
Chpt 11 *

assume = take (power or responsibility)

Definitions:

(1) (assume as in: I assume it's true)
to accept something as true without proof
(2) (assume as in: She assumed power)
beginning to take power or responsibility
(3) (assume as in: She assumed a false identity)
to take on (adopt, wear, strike a pose or appearance of) -- often while pretending or disguising
(4) (assume as in: assumed into heaven)
to take up or receive someone into heaven
(5) (meaning too rare to warrant focus)