A number of brown dwarfs have had 'surface maps' created using the light from those stars.
In 2013, observations of 2MASS J22282889–4310262, a brown dwarf 35 light years away, were published. These were made using the Hubble and Spitzer space telescopes and were able to show changing light patterns and distinct layers of material at different altitudes in the atmosphere. This provided evidence for textures but not necessarily banding in the atmosphere. I believe the Hubble has carried out other observations of brown dwarfs with the aim of determining their surface details.
In 2014 Luhman 16 A and B, a brown dwarf binary system, 6.5 light years from Earth, were imaged using the VLT CRIRES spectrograph. Luhman 16B was found to have patches perpendicular to the plane of rotation. Luhman 16A was found to be featureless at the frequencies observed.
Earlier this year, a paper was published describing how the VLT had been used again, this time employing polarimetry, to detect Jupiter-like banding on Luhman 16A.
The paper here describes modelling based on observations that indicate Jupiter-like cloud bands (page 13).
So there does seem to be mounting evidence that brown dwarfs have stripes. The accuracy of the artists' impressions is something we'll probably find out in the future.
UPDATE - January 2021
A new study of Luhman 16 A and B by Apai, Nardiello and Bedin has been published. They applied a 'novel photometric approach' to TESS data and found that we are viewing them at angles close to their equatorial planes and that they look 'strikingly similar to Jupiter'. The paper at the Astrophysical Journal is here but is paywalled.
Last update, I promise!
This is an image from the Apai, Nardiello and Bedin paper that was reproduced at Centauri-Dreams.org. The preprint of the paper is available for free download at Arvix.