We are making an adventure that we wish to publish on DMguild and maybe in print. The Goddess Shar comes up in this, is this allowed?
Game: 5e dnd in the forgotten realms setting.
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When it comes to the licensing of publishing D&D material you have two options - you can either publish via the Wizards-of-the-Coast-affiliated DMs Guild, or you can publish under the OGL (Open Game Licence).
If you publish your adventure on DMs Guild, the answer is yes. According to their licensing FAQ, DMs Guild products are allowed to use the Forgotten Realms campaign setting, which is where the deity Shar comes from:
Under the DMs Guild program, you can publish D&D material that has no setting or uses the Forgotten Realms, Ravenloft, Eberron or Ravnica settings.
However, if you publish under the OGL, you cannot:
Under the Open Game License, you can typically publish material that has no setting or uses your own original setting.
The OGL only grants you a licence to use material designated as Open Game Content, which includes most of the content in the 5e System Reference Document, but doesn't include any named deities from specific D&D settings. The licence as written in the 5e SRD (as of 2016, the most recent update) specifies a long list of things that are "Product Identity" and not "Open Content" (emphasis mine):
The following items are designated Product Identity, as defined in Section 1(e) of the Open Game License Version 1.0a, and are subject to the conditions set forth in Section 7 of the OGL, and are not Open Content: Dungeons & Dragons, D&D, Player’s Handbook, Dungeon Master, Monster Manual, d20 System, Wizards of the Coast, d20 (when used as a trademark), Forgotten Realms, Faerûn, proper names (including those used in the names of spells or items), places, Underdark, [...]
All of the rest of the SRD5 is Open Game Content as described in Section 1(d) of the License.
So the proper name of a character or deity from an official D&D setting is part of the "Product Identity" you are not permitted to use under the OGL. The licence goes on to clarify that Product Identity means:
[...] creatures characters; [...] depictions, likenesses, formats, poses, concepts, [...]; names and descriptions of characters, [...] personas, likenesses [...]
So you also need to be careful about plucking a deity straight from FR and simply changing the name, if you describe them in a way which is too similar to their depiction in official material.
Note that in order to print and self-publish D&D 5e resources you must be OGL-compliant - there's no legal avenue for you to print and sell your own books that use non-OGL content, like the name and likeness of the deity Shar. If you want to include that content, you have to go through the DMs Guild program.
Also note that if you do publish via DMs Guild, you also have to agree to only publish that content via DMs Guild - you cannot print and self-publish the same product separately even if it is also OGL-compliant. (I wasn't able to track down an explicit statement to that effect on the DMs Guild site, but I've seen it confidently asserted by others in several places - presumably it's in the text you have to agree to when you actually go to publish.)
If you want to self-publish, you'll have to forgo DMs Guild and rewrite your adventure to ensure it doesn't refer to any D&D IP that isn't in the SRD. If you're happy to only sell via DMs Guild, you can use all Forgotten Realms material you want.