That depends on your dialect. Can you hear the difference between “Mary”, “marry”, and “merry”? How about “cot” and “caught”? “Aunt” and “ant”? “Pen” and “pin”? For each of those, there are some dialects which distinguish them, and some which don’t.
I once had a dinner table debate with my sister over the names Aaron and Erin. I was the one who thought they were pronounced differently, and my mom agreed. Dad didn’t weigh in. But she stubbornly stuck to her guns that she didn’t hear a difference even when I tried pronouncing them the way I knew. So I definitely understand where this is coming from. Not sure about this particular example, though.
Yeah, for me, Aaron and Erin are pronounced the same. Same with names like Carrie and Kerry. Yes, I know what the difference is and can pronounce it in careful speech, but my dialect merges those sounds, and I don’t really “hear” them. That is to say, while I do appreciate the difference and can hear it with careful listening, in spontaneous speech my brain merges them all together. It’s not a distinction in my dialect.
While “gulf” and “golf” are distinct to me, I can hear it in my head in such a way where in a certain accent it may be difficult to tell the two apart.
Actually, now saying it outloud to myself, they are pretty darned close in my dialect. I think of them as being quite distinct, but actually saying it, I wouldn’t be surprised if someone mistook my “gulf stream” for “golf stream.”
To me, I can hear it either as “golf stream” or “gulf stream,” depending on what I’m expecting to hear. Actually, even with the first pronunciation, it can be ambiguous to me.