A gift to you is tax free and not reported on your return. The giver should file a 709 gift tax form.
The problem is that it’s just 50% of the equity from a house sale. BUT the house was not in my name and I didn’t receive any tax forms.
If you were not the owner, then what probably happened is the owner sold the home, and gave you some of the proceeds. That's not a taxable even to you, and it doesn't matter from a tax or law point of view, what the giver did to get the money that they gave to you.
If you are concerned that you might have been a part owner, and part of the gain (profit) from the sale is taxable to you, you should start by seeing an attorney to review the deed and other documents of sale, to clarify your position.
The owner of the house is not allowed to shift half of the tax liability, on any taxable gain, from him to you, without some legal reason.
A common situation is the sale of a deceased relative's property where the new owner wants to share the proceeds with other family members. Since there was no legal obligation to to so, the money transfer is considered a gift for tax purposes (not taxable to the recipient of the gift).
There is usually little or no capital gain on the sale of inherited property due to the step up in cost basis