In the context of the question (mains wiring, greater than 50 volts, etc) NEC stipulates that white-marked conductors be used only as a grounded conductor (ie neutral). Referring to the 2017 edition, the requirement is found in 200.7(A):
200.7 Use of Insulation of a White or Gray Color or with Three Continuous White or Gray Stripes.
(A) General. The following shall be used only for the grounded circuit conductor, unless otherwise permitted in 200.7(B) and (C):
(1) A conductor with continuous white or gray covering
(2) A conductor with three continuous white or gray stripes on other than green insulation
(3) A marking of white or gray color at the termination
Exceptions immediately follow. Paragraph 200.7(C)(1) is applicable to this question:
(C) Circuits of 50 Volts or More. The use of insulation that is
white or gray or that has three continuous white or gray stripes
for other than a grounded conductor for circuits of 50 volts or
more shall be permitted only as in (1) and (2).
(1) If part of a cable assembly that has the insulation permanently reidentified to indicate its use as an ungrounded
conductor by marking tape, painting, or other effective
means at its termination and at each location where the
conductor is visible and accessible. Identification shall
encircle the insulation and shall be a color other than
white, gray, or green. If used for single-pole, 3-way or
4-way switch loops, the reidentified conductor with white
or gray insulation or three continuous white or gray
stripes shall be used only for the supply to the switch, but
not as a return conductor from the switch to the outlet.
These citations do not address the extent to which the mark may or must conceal the original marking of the conductor. It might be useful to survey the code for other instances in which re-marking is addressed to look for a pattern. In 250.119(B)(3), regarding the marking of a conductor in multi-conductor cable for equipment grounding, the code states
Identification shall encircle the conductor. In section 690.31, regarding wiring methods permitted for PV systems, there is mention of
separate color coding, marking tape, tagging, or other approved means but again no discussion on the extent of coverage of the original conductor marks. One can understand that tagging would provide a very minimal degree of coverage, however.
Absent specific guidance on the topic, the general requirements of being durable, of good quality, executed in a workman-like manner, etc should be maintained. I see nothing that would lead a person to believe it is necessary to make any effort to conceal the original markings of the conductor.
In my opinion, it would be good practice not to fully conceal the original color or markings of the conductor so as to create awareness that the conductor is reidentified. This can serve as warning in case the cable should become exposed in a new place, or in case its marking in another place should become removed.