Clean it up with wire wheels on an angle grinder first.
Then carefully grind the edges clean with the angle grinder and a grinder disc.
Lastly clean up the face. Start wit a flap disc on the grinder, and see how bad it is. Don't remove any more metal than is necessary on the face.
How long and what dimensions are the stake? ( the part below the flange)
Some of those post anvils were set in a big and heavy cast iron base with a fitted hole for the stake.
If the anvil will be set up in a shop where you will keep it, make a base from concrete. There are three ways ( in order from best to worst):
1) Take a wash tub and suspend the anvil over it with the top level. The end of the stake should be at least 15cm from the tub bottom. Pour concrete in the tub until it is at least 10-15cm above the flange ( filling the whole tub is best). This will make the anvil even heavier....and very sturdy. This is the simplest and strongest method. Using the wash tub handles, two strong guys can move it around a bit, but it won't be portable for much distance. You can put a plastic trash bag or BBQ grill cover over the anvil if it sits out in the open. I doubt it will walk away with the whole thing weighting 250 pounds or more. A chain around the anvil and a tree would prevent that happening, too.
2) Weld up a sleeve box that tightly fits the stake ( grind the stake clean and smooth first). Make a wash tub base as above with the sleeve cemented in the center. This will allow the anvil to be placed in the sleeve socket. It will only be as sturdy as the tightness of the socket. This will allow you to remove the anvil and just leave the tub of concrete where you do your forging.
3) You can use a stump with a hole bored in it a bit undersize and pound the anvil in the hole. Grind the stake end clean and taper it a bit if needed. Use a sledge hammer and place a piece of metal or wood on the anvil face to keep from damaging it when you hammer it into the stump. It will take several people to do this right and safely. Unless the stake end is long and tapered, using a stump may not be as sturdy as the tub of concrete method. Removing the anvil from the stump may be difficult, too.
When using a stake anvil, try to keep most of the heavier forging done directly over the post.
