I like it. I don't associate it with lower class parents; I've known 3 & all were middle class.
It used to be on my favorites list for a short while but dropped off due to my sister's former friend
Bethany. It feels a little plain & dull to me but it is a sweet name & never was super popular. Plus you could use the nickname
Beth, which I adore. I think I like
Beth better than
Bethany & mostly like
Bethany for the nickname.