Do the sentences above sound equally natural to the modern-day English speaker? Or is one of them more preferable? Or had I better stick to "can't remember" instead?
I find "I've forgotten her name" and "I can't remember her name" most natural. "I don't remember her name" would be my next preference. I would understand "I forget her name", of course, but it would sound old-fashioned.
Do the sentences above sound equally natural to the modern-day English speaker? Or is one of them more preferable? Or had I better stick to "can't remember" instead?
Either one is fine in American English. We're more likely to use the second if forgetting her name is unexpected: We had a passionate love affair in college. I can't believe I've forgotten her name!