If I inherit $20,000 without being named in the will, is it still an inheritance?

You either received a gift or an inheritance.  Neither is taxable.

(And it sounds like a gift - e.g, the owner sold the property, died, and funds transferred to the estate were given to you.  if not in the will the transfer to you would have been a gift from whomever the beneficiary was that gave up the funds.)

Thank you.  I thought a gift had to be $10,000 or less.

Reportable Gifts are those that exceed $14,000 given by one living person to another person.

In almost all cases, the Beneficiary pays no Inheritance Tax, nor Estate Tax.  

However, if you inherit an asset that itself will create income, you are liable to pay income taxes on that income generated.

Since the Estate bore the transaction of the sale, you need not report a sale of it as an investment asset. You either were gifted or inherited the cash.

The only question of Inheritance Tax relates to a very few states, and then it depends on relationship.  Where do you reside?

Texas

No Inheritance Tax in Texas.

A Will might bequeath less than 100% to named beneficiaries, in which case the laws of your state determine who gets the remainder of the estate. That would be an inheritance.