This could be a major problem and I would get it rectified ASAP. Most airlines, if not all, will not allow passengers to travel where the name does not match. They may make allowances for slight differences (I travelled with a friend once and I mis-spelt her name when making the booking i added an "h" where there wasn't one and BA were able to make a note saying that the name had been mis-spelt on the booking and she was able to travel) however in your instance the name is completely different and will most certainly need a ticket re-issue.