More likely than not, this will just mean that you are covered through some sort of group contract the hospital has with one of the major insurers. You would have a policy with your name on it and you would be covered just like anyone else. The limits sound typical.
The issue, you have to look at is how your contract with the hospital deals with the issue of 'tail' coverage (or the more precise insurance term would be 'reporting endorsement') The way 99% of malpractice insurance is written these days, it only covers you for claims brought against you WHILE YOU HOLD AN ACTIVE POLICY ('claims made coverage').
So, the problem arises once you leave that hospital, if someone you harmed during your tenure there brings a suit 3 years later (average time), you are not covered. Malpractice insureres offer a special policy (the 'tail') which if you buy it covers everything reported after you terminated the malpractice policy. This 'tail' typically costs between 1-2.5 annual premiums. This can easily be 50-100k depending on your specialty. Make sure that your contract with the hospital addresses this issue. If it is not addressed, buying the 'tail' is YOUR responsibility (or buying 'prior acts' coverage from the insurer you join afterwards).