Why do you two want the house to be in your name only? There's no obvious tax benefit. There's no inheritance tax payable when one spouse dies and leaves property to the surviving spouse, whatever the value of the property.(You both should have made wills, by the way ).If you were ever to divorce, the court would not be stopped from dividing the assets as the court decided, regardless of whose name was on the deeds.
The lender will certainly refuse to comply. Lenders don't want to lend to one of a couple who simply cohabit, never mind being married ! That's mainly because the lenders are worried that the other one may make a claim to stay resident in the house if the couple split or a monetary claim to a share of the property on an equitable basis..