Shakespeare uses a lot of blank verse. I get it that there's no proper rhyme scheme, but there is meter. Why is it called "blank"?
OED has blank verse as first appearing in 1589 citation:
verse without rhyme; esp. the iambic pentameter or unrhymed heroic, the regular measure of English dramatic and epic poetry, first used by the Earl of Surrey (died 1547)
1589 Nᴀsʜᴇ in Greene Menaph. (Arb.) Pref. 6 The swelling bumbast of bragging blanke verse.
Its earliest meaning for blank is "without colour", and has citations as early as 1325, although the word is derived from French blanc, white, which would have arrived with the Normans.
1. White (obsolete, and chiefly in specific uses, e.g. blank plumb white lead, blank falcon a ‘white hawk,’ i.e. one in its third year); pale, colourless." [my emphasis]
Sense 2 (the next, chronologically) only has citations from 1555, so the "white; pale, colourless" meaning was well-entrenched in the sixteenth century.
Given that the first use of "blank verse" is well over 400 years old, finding why that term was chosen is likely to be impossible. It's entirely plausible that blank verse was seen as colourless when compared to rhyming verse, a pale imitation, even though later authors appear to disagree:
1784 W. Cᴏᴡᴘᴇʀ Let. 11 Dec. (1981) II. 308 Blank verse is susceptible of a much greater diversification of manner, than verse in rhime.
1874 A. H. Sᴀʏᴄᴇ Princ. Compar. Philol. ix. 385 Our greatest poems have been written in blank verse.
Bearing in mind Andrew Leach's answer above and
Its earliest meaning for blank is "without colour",
It may be worth noting that it is likely that "blank verse" = that which gives the outward appearance of verse.
This would coincide with, OED's entry for colour:
II. Figurative senses.
Senses relating to outward appearance.
- Outward appearance; show, aspect, or semblance of something, esp. as justifying a particular judgment, course of action, etc.
a1325 Statutes of Realm (2011) x. 64 Þat no religious..ani londes ore tenemens buche ne sulle, ore þoru ani colur of ȝifte..oþer on ani maner þoru art ore engin nimen an honde to hoem to apropri.
(That no religious [institution/person]...any lands or buildings buy or sell, or through any colour of gift ... )
1980 J. Gage tr. J. W. von Goethe in Goethe on Art i. 49 That is just the trouble, when good minds get hold of such false principles, which have only a colour of truth, and expand on them.
The OED adds
Frequently, esp. in later use, with the implication that the appearance is false and used as a pretext. Now chiefly in legal contexts
Thus originally it simply meant "an appearance of" thus "blank verse" = with the appearance of verse, in which "verse" would mean "poetry that rhymed.