It would definitely bother me! My first name is very common but spelled a little different so it is common for people to misspell it. I usually give them a couple of chances and the occasional mistake/autocorrect, but if it happens frequently, I completely feel like they don't care at all. My T did it once but she sent the email from her phone so I'm assuming it was autocorrect or she just sent it quickly.

This is a bit of a tangent but I had a teacher in high school who misspelled my name all year even though we had daily quizzes where she obviously had to read my name and enter my score in the grade book, every day. She taught AP European History and was extremely intelligent but I had trouble respecting her because she didn't pay enough attention to get it right.