I think it's cute and quirky. Like most one-syllable names, I think it fits best with a mn with three or more syllables, like
Wren Josephine,
Wren Octavia,
Wren Isabelle,
Wren Lucinda, or
Wren Juliet. Using it as a mn, some combos I like
Lola Wren,
Olga Wren,
Isabella Wren,
Mary Wren,
Julia Wren,
Louisa Wren,
Amelia Wren, and Tzipporah
Wren.