Dylan made two important career moves in August 1962: he legally changed his name to Robert Dylan, and he signed a management contract with Albert Grossman. (In June 1961, Dylan had signed an agreement with Roy Silver.
Two weeks too early for tattoo touch-up? You can get a tattoo touch up as early as 2 weeks, especially since it sounds like your tattoo is already done with the whole scabbing/peeling phases of healing.
With a new tattoo you should focus on keeping it protected while the skin heals. That means no shaving, never touching it without washing your hands first, do not scrub the area, and being generally careful with the site. Once the skin is healed completely, which can take 2-3 weeks, then it's fine to shave over it.