What is the name of my drawing style? Black and white?
Black and white is the colour scheme of your drawing - it is never a style.
The medium is ink on paper, if digitally cleaned up and printed it can be described as a print (and you might want to consider working in (limited) editions).
The technique, depending on your drawing method, seems to be free drawing, akin to free writing (and in that case an intentional form of doodling), or 'automatic drawing', the drawing counterpart to automatic writing.
Since these methods usually produce an idiomatic decorative pattern (as user agarza mentions in the comments, it is similar to henna drawings, or mehndi), they can be used to describe a style as well, simply because it will tell people what to expect. But a better way to go about it is to see what makes your artwork yours, what is unique about it, and either combine that with 'doodling', 'doodles', or 'free/automatic drawing', depending on what kind of audience you want to appeal to.
For instance, your drawing also reminds me of a more abstract and asymmetrical and less geographical form of the luscious horror vacui ornaments and illuminations in manuscripts:

Gothic Ornament with Putti and Acanthus Leaves, 19th century.
Source.
Click for larger version.
Hence, 'ornamental free drawing' could be a way to describe your artwork.
Ultimately, you know best what you want to achieve and what kind of clients you want to attract, so play around with the suggestions given here in the comments and answers until you find something you think is appropriate for your artwork.