Transferring your mom’s property into your own name could be risky business—unless the document specifically provides that you can do it. Otherwise, as the agent under your mom’s power of
attorney, your job is manage the property for her benefit, not transfer it to yourself.
If you are serving as an agent, and your mom is not incapacitated, but just wants you to manage her property, she can make a gift of it to you directly if she wants to do that.
If you are currently serving as an agent because your mother is incapacitated, you are limited to what the document permits. The document may give you the ability to make a gift to yourself of some property, usually limited to the annual gift tax exclusion, which is currently $13,000 per year. This is done primarily for tax planning purposes--as a way to transfer assets without paying gift taxes.
Often, however, powers of attorney forbid that very form of gifting, so you should check the exact wording of the document you hold.