Register your Domain Name
Remember you are NOT buying the domain name but renting it year after year. If you cease to pay rent on your domain name YOU WILL LOSE IT and it is very likely a domain name squatter will rent it and you will have to pay them $$$$ to get it back.
Document and protect access to your organization's internet accounts. Create a password protected document (You can create a password protected a Microsoft Word Doc) that has all your organization's internet accounts (website, Social media etc..) usernames and passwords. Make sure two people in your organization have access to that document at all times. If not, Murphy's Law (and past experience) says the person who has the password will die or move to Florida and your organization will not be able to access the document and you will lose all your accounts.
So that being said...
A couple of places you can register your Domain Name. (their are hundreds of other places you can register a domain name).
Picking the right domain name is important
Choose a domain name that is easy to type.
Go with a ".ORG" or ".COM" or ".museum" domain name extension
Keep It Short, Simple, and Predictable
no hyphens, no underscores, no complicated words as part of the domain, or any other punctuation
just words — avoid using numbers or abbreviations unless absolutely necessary
Try using keywords that describe your business, location and/or the services you offer.
Domain Name Examples
GOOD
acmehistory.org
acmehistory.com
acmecountyhistory.org
acmecountyhistoricalsociety.org
acmemuseum.org
acmefactorymuseum.org
achs.org
acme.museum
BAD
acmecohistso.org
acmechs.org
acme-history.org
acmehistory1845.org
historyisus.org
acmehistory.biz
acmezon.com