How to upgrade individual account to family?

VOSSBoys2003,

Unfortunately the Family Plan has been discontinued. I've included a link for the

Family Plan Conversion FAQ explaining the transition. At this time, there is no plan's for families on the Xbox 360 console. With the Xbox One console, a new plan was introduced called Home Gold where only 1 account needs to have gold for the entire family
to enjoy the gold benefits. Let us know if you have any other questions or concerns.

Did you upgraded your account to a Gold Subscription or bought a Family Gold Pack? You shouldn't have been able to purchase a family gold pack as it has been discontinued and accounts are being converted to individual gold accounts making way for Xbox One's
Home Gold plan. If you already had a Family Gold Account and your accounts haven't been split into individual gold accounts you can review this

Add/Remove FAQ for the Family Pack. As an individual Gold subscription you cannot add members. You can review this

FAQ for more information about the conversion to the Xbox One Home Gold plan.

I know on some games, such as minecraft, that you can split screen with two accounts. My son and I can do this and we do not have a family account, just two individual accounts. I am also sure you can upgrade your individual account to a family account.
I was able to find this for you as well:

Xbox.com steps: Convert your membership on Xbox.com

1. Go to My Account.
2. Under Membership & Content, click Upgrade/Manage Account.
   
   Note If you are not signed in, you will be prompted for your Microsoft account (formerly "Windows Live ID"). Type the Microsoft account information for the Xbox LIVE account that you want to be the primary account holder for your Gold Family
   membership (an adult account).
3. Select Gold Family (where available), and then click Next.
   
4. Follow the on-screen instructions to convert your membership to a Gold Family Pack membership.
   

The only thing that changes when you get a Gold Family Pack is that you plus three other family members can get One full year of XBOX Live service for $99 (4 x 1 XBOX Live Year) - which is an awesome deal if you're a family. You would get to be the primary
and the rest of the family members can get added as secondaries or you can make another parent account, that choice is yours. You get to track your families gaming time (how much time they spend playing games, what games they play etc) as well as the ability
for the parent (you) to be able to distribute Microsoft points to the other family members accounts (which is an awesome feature ). That link that SONIC SCREAM 07 posted will basically detail more of what I just said and much much more, definitely worth
it if you've got a large family that all plays XBOX's. If you decide to get more XBOX's they can recover their gamertag to those other consoles and still have the year of XBOX Live active since they are still under your family account (which is also one
of the other great features of the package)

All of the information about the Family Pack can be found

here.

But to answer your question, yes you can keep your existing gamertags and everything associated with them.