not if the lease prohibits it.
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Dear can they do this?
Not if the lease specifies a particular use and the new name and new use are not covered by the lease.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
I'm not sure how you've determined from the sign on the door that the tenant is using the premises in a manner prohibited by the lease but it seems to me another issue is that your tenant (the one whose name is on the lease) may be subletting the premises to this other company. Generally a lease for office space would contain at least some restrictions on the tenant's ability to sublet the premises. So your tenant may be violating multiple lease clauses.