Do I need to get a new lease in my name for existing tenant

[Calvin Rappard]

I just bought my first rental property in the Chicago area northwest suburbs (Cook county). The current tenants have a lease until end of January, which I will honor. In the closing docs, there was a document that signed over the rights of the current lease to me. Should I still do some sort of addendum to the existing lease to have it in my name, or am I okay to leave until renewal in January? (Existing tenants intend to stay on.)