CLERIHEW

The clerihew, invented by Edmund Clerihew Bentley, is a 4-line structure with couplet rhyme.  It requires no specific meter or syllable count.  It is not titled, but the first line must name the person the poem comments on.

Another source describes the clerihew as a whimsical, 4-line biographical poem.

Here are two examples:

Sir Humphrey Davy
detested gravy.
He lived in the odium
of having discovered sodium.

Sir Christopher Wren
said, "I'm going to dine with some men."
If anyone calls,
say I'm designing St. Paul's."