If you refinance out of the construction loan into the new permanent financing loan in just your name - then yes. You would just need to be able to qualify for that permanent financing "take out" loan on your own.
Free Mortgage Advice & Pre-Approvals (FHA, VA, USDA, Fannie, Freddie, Non-Prime, Construction, Renovation/Rehab, Commercial) since 2002
Located in Southern California and lending in all 50 states