I am in a common law relationship and we are both on the title/mortgage. How do I transfer the home/mortgage into my name?
The kind of relationship you have (common law, married, sister and sister, parent and child) is not important for this question. You and some other person own the house together. You and this other person also have agreed to pay the bank the amount of the loan balance.
Neither one of you alone can remove the other from ownership or responsibility for debt repayment.
Both of you must sign a deed which transfers the ownership to just one of you. Both of you must obtain the permission of the lender to remove one of you from the loan documents.
If you don't act together, the remaining possibility is a very long and very expensive lawsuit to persuade a judge to put the ownership is just one of your names. There is virtually no probability that a lender will permit one of you to be removed from liability for the debt.