I'm in the midst of writing a story involving Cyric and Tharizdun butting heads over a group of mortals attempting to obtain one of Cyric's toys and destroy it. (based on a 2 dungeon master, dungeon me and some friends did a while back)
I just wanted to know if it would be legal for to use the two god's names.
All FR gods and other setting proper nouns are the intellectual property of WotC - probably copyright, maybe some trademark, maybe even some trade dress. The specifics aren't all that important in this case.
Technically, legally, and unless you have a bunch of money and lawyers to try to fight it, you need permission to use them. This kind of use is NOT protected by Fair Use nor by the OGL nor by any of the other things people think it is. If you are trying to publish a novel using their characters or setting, they will crush you.
However, no offense meant, but due to the 6 grammatical errors in just the 3 sentences of the question above, I assume you are just planning on writing fan fiction for your/the Internet's enjoyment and are not a professional novelist.
You can take one of two paths to writing FR fanfic.
Use a WotC community use license - I believe this is the latest one; it's for fansites. Read through it and see if you think it covers your use case (needs to be free and non-offensive), and then comply with it. Or possibly releasing it via the Dungeon Masters Guild which also has a bunch of restrictions (you can't publish it anywhere else).
Just do it. They will ignore you unless you try to make money or otherwise make a pest of yourself. It's just as "illegal" as writing a novel for publication, but they have bigger fish to fry and damages are $0, so you're going to be fine 99.9% of the time. If you write the world's most popular Cyric/Tharizdun slashfic they might send you a Cease & Desist order and/or send a DMCA takedown notice to your ISP - that's what they did to a couple of people writing character generators and power card things during 4e. They are within their legal rights to sue you - but they're within their legal rights to sue you no matter what you do. If you're writing FR fanfic for free - well, go Google for it, there's a bunch and no one's getting lawyers air-dropped on them.
You cannot copyright a name.
Still, this doesn't mean you can use them freely, because characters can be copyrighted. The deities in Forgotten Realms are no doubt fictional characters with individual characteristics, so they are subject to copyright.
This means that, you can use the names, but if you also borrow the characteristics (appearance, moral alignment, deity level renown and power etc) so that they start to resemble the gods in Forgotten Realms, then you start stepping into grey area.
How much grey is illegal, or whether your use is fair (most likely not), is ultimately up to the court. The same goes for how much you need to change them to make them something different.
P.S. OGL would not grant you the rights for various reasons, either:
Names can also be made a trademark, but you don't have to worry about trademark if you are just using the character concepts in the adventure.
Using those gods names in your story can be legal. The key word is free. If your content is released for free then, assuming you meet the other requirements listed by WotC, your content can be released under the Fan Content Policy of WotC.
Other requirements of the Fan Content Policy include:
Releasing content on DMsGuild gives WotC 50% of your proceeds and gives you rights to use any of their existing Forgotten Realms content but you cannot sell your story anywhere else after that. DMsGuild focuses on modules and supplements rather than stories - so you may need to reframe your content to fit the products they typically sell.
The Standard Reference Document (SRD) lists all the D&D content you can use for free via the Open Gaming License as long as you cite the OGL and adhere to it's requirements. The link here outlines how to tell when your content must be released by DMsGuild or when you can use the OGL. I searched the SRD and Cyric is not listed. As noted at the table in that link, your story uses Forgotten Realms which is content only available through DMsGuild and is not in the SRD. The only pantheons of deities in the SRD are Celtic, Greek, Egyptian and Norse gods.
Copyright does not cover names, facts, or vague ideas. However, the FR deities are almost certainly not legal for use:
When I was in class, my copyright law professor used to say (a slightly different version of) the following:
Copying someone's work verbatim without their permission is infringement, unless it is fair use.
While one can argue that you aren't copying someone's work verbatim, that's overlooking the concept of copyright law: copyright law cares more about the essential qualities of a work than its literal format: if I were to copy a book and simply run it through Word's thesaurus to change all the words to a synonym it would still be an illegal copy.
Using D&D content in a third-party work without permission is almost certainly going to be infringement.
With this in mind, you have two ways to continue:
The first option requires some significant changes, but not as many as you'd think. Since you probably don't deal too much with the histories of the deities involved, name changes may actually be sufficient for legal protection.
The second option is bad, but if you're writing an entirely non-commercial fan work, you may be able to let it skirt by. If you hope to sell your work, however, you will likely be sued, while a non-commercial use will typically see a cease and desist notice (again, this is not a legal opinion or advice, just a commentary on the way things are; if you get sued you're on your own) instead of a lawsuit because copyright law is expensive to enforce.
