Are you worried that the contractor will file a mechanic's lien even if you are paying off the loan as agreed? First, the loan agreement should be in writing. Second, you could ask the contractor to waive any right to a mechanic's lien (in writing also) so long as you are paying off the loan as agreed.
Yes, they can still put a contractor's lien on the property, even if your name is the only name on the contract itself.
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The contractor seems to want to give you a loan instead of an installment payment plan for the balance as avoidance to non-payment if a contractual dispute arises, so you may want to consider that concern. The contractor can place the lien on the property he works on, and it avoids the legal issues of ownership.
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