I've been unable to find any reason, either in universe or out of universe as to why the hammer changes name. The best I can come up with are some scenarios where the name change might have occurred.
Possibly just a minor mistake by King
King could have just misremembered Firebeard's hammer, the Hammer of Fate as the "Hammer of Firebeard".
FirstCape is correct. The other is wielded by Thorgrim Grudgebearer as it was passed down before Grimnir left.
If any of you can remember back far enough, they used to have the magic items on cards in the code books. Gotrek's Axe is how it was named there was identical to Thorgrims axe. No armor saves allowed except by magic armor and that was at -3, d3 ...
The name was never revealed, you've pretty much described all we know of the axe, except that:
So we know it was forged as you said, but that is it!
I used to have the model for it as well, and I think it was always just known as "Gotreks Axe" or "Runesmith Axe" in game.
Deep inside Gotrek and Felix - The Anthology, is a short story called Kineater. It takes place between the events of Giantslayer and Orcslayer.
Kineater takes place in the Orge Kingdom, but Gotrk and Felix have travelled directly from Ind as mercenaries with an Arabyan caravan.
One of the characters is perusing Felix's journals and points out the following,...
I asked my good friend David Guymer (Author of CotD, The End Times and Kinslayer) to answer this for you:
Q. Quick question; Do I need to read City of the Damned before starting The End Times and Kinslayer?
A. Quick answer - No :) Quick-ish answer, no but there are a few characters from CoTD that reappear in Slayer
The conclusion to the story of Snorri Nosebiter does occur in Kinslayer. Previously Snorri had forgotten his shame and the reason he became a slayer. In this book it is revealed along with if he in fact finds his doom. I do not recommend looking at the spoiler below as it may ruin the story for you, but I will supply it as proof of answer to this question.