No, that’s a wild rose flower. The word ‘briar’ refers to the thorns on the stalks as in “Dammit I snagged my sleeve on that briar”
That’s why ‘she’s a briar’ is used as a description in some places for an abrasive, thorny, person.
If you like the sound I’d suggest Bryony, Bree, or Brianna. If you like flowers I’d suggest Roslyn, Rosalind, Rose, Rosanne, Lily…