Judith ,
Its a PALM .
Its a Sabal Minor ( var.Louisiana )

They both can survive brief dips below zero.
They are a rare find outside of the deep south.
I have been to Senoia,GA many times. Its a very small spot in the road and about 30 miles south of Atlanta.
Its claim to fame is the GREEN PLANT NURSERY .
Thats where the palm came from I imagine.
The down side to the above mentioned cold hardy palms is they dont trunk very much. They are BUSH LIKE palms.
With that Sabal Minor ( var.Louisiana ) you have , you can expect Large Palm Fronds ( about 3 or 4 feet tall ) to erupt from the ground to display a very exotic and tropical look.
I dont know how big yours is , but it sounds like its potted and perhaps small. Thats OK ..in three or four years you will have a real beauty. It was very nice of someone to swap that palm off . Its fairly valuable , a 5 gallon potted plant cost atleast 50 dollars in most nursuries in the south.
Plant it out in the spring in an area where it will get lots of summer heat and sun. Plant it in an area where snow melts first and where snow dosent linger . This is a microclimate.
The south side or the east side of your house would be great and up near the house foundation would be real good.
It will have to be protected for the first year or two in winter. This means you may have to throw a box over it during ice or snow storms or you could just snap off a few pieces of ever green sprigs from a tree and insert them into and around the palm. A good dose of mulch will be necessary also around the base of the plant if you live in an area that has ground freeze in winter.
This is a great palm for you to enjoy . I promise that you will be proud of it one day.
I have many here : Texas , Oklahoma , Louisiana , S.carolina strains , I even have a Tennessee strain from Quebeck , Tennessee. These palms are awesome and normally get about 4 feet tall and the fronds may fan out about 4 feet . You can plant flowers and other goodies beneath them. They will seed and mine has produced tons od seed in the past.
They love boxed plant food (granular..like tomato , etc..
and they respond to miracle grow but they adore horse manure scattered around the base of the plant . They like lots of water for the first year or two and during dry spells.
The minors can produce trunks of a few feet in the most southern areas and in areas that they are native to in the outter banks regions of NC.
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There are huge ones in the coastal Lou. area.
Here are some naturalized sable minor palms growing along a rural road near Sparta , Tennessee.
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The seed from the mother plants ..up the road..started these.
Maybe if you find yourself 'bitten' by the palm bug...you could try one of these trunking palms.
The Trachycarpus Fortunei Palm..aka chinese windmill palm..NOT chinese fan palm.
I have been growing these here also for years :
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Thanks, but I'm hoping to hear from the person who brought this to the swap. I really don't hink it's a palm---it looks NOTHING like the pics you've posted here.

Someone who bought a Sabal palm in Senoia, GA, probably used the pot to put something in for the swap. Or used a pot they got from someone at another swap who bought a palm, etc. Pots can have many lives.
Which doesn't help at all when it comes to identifying the plant. Post a picture of the plant and someone might recognize it.

Nope, the label's not on the pot, it's written by hand on a stake and stuck down into the soil. It may well BE a palm, if they grow up to look very different than they do as babies...

Ah well---picture time!

Judith , does it look like this ?

or perhaps a better view :

Yes--it DOES look like the bottom pic! Does this mean it IS a Sabal palm? If so, can I plant it outdoors here in zone 7a? Should I plant it this spring, or keep it in a pot until it's bigger?

Hi Judith ,
I was almost certain it was the sable minor since it came from Senoia but Madmouser made a great point about pots being used again..lol..then you stated it was stick labled..lol..
Your palm is the sable minor.
It has many varities . A popular one is the sable minor various Louisiana , thats where its most likely found , but also native to coastal NC.
They are hardy and like my posts above states , can live here with very little trouble.
Its also called Dwarf Palmetto ( check that out in GOOGLE )
also blue palmetto and sable minor aswell.
The sable minor (var.Lou.) that you have gets a small trunk after several years and the palm fronds are somewhat larger than the other varities . In about 3 or 4 years you should see quite a palm. They love sun and water and plant food.
They will need a little cold protection for about 2 years but it isnt much trouble.
The reason these palms are so hardy is that the trunk ( ever so small ) stays in the ground and dosent come up , thus keeping it warm during winter , just those awesome giant fronds grow from the ground . Keep in mind , palm roots DO NOT disturb water lines , gas lines , house foundations etc. the roots simply bypass anything like that , so dont worry about that underground trunk. Be sure to find a good place to plant it because they dont like to be moved. Remember , it will get about 4 feet tall ( those fronds ) and the fronds may fan out about 4 feet also.
Your specie is known to push that trunk on up a couple of feet or more but in our climate , it would take many years.
Its often said that because we do have fairly cold to cool winters , we should plant these type tropicals as large as we can find them because they are slow growers but our hot summers is what they really love and makes them grow .
That is the sable minor , the sable major has other names too : The Sable Palmetto ( its big brother ) also known as the cabbage palm . This palm is the state tree of SC and FL. Its the palm tree you see alot in florida .
I have three of the majors at my house ( sable palmetto )
These trunk but arent as hardy as the minors we are speaking about .
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I planted this transplant on easter sunday and its doing fine here in z7 Tennessee hill country.
I planted these about 5 years ago from 5 gallon pots and these two are trunking now :
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You could certainly keep your little palm potted for another year or so but it will grow faster in the ground. They will be slow at first , it takes the second year before they KICK IN GROWTH . They love lots of water and sun and if you keep it potted you will need to do that , with pot drainage of course. Id plant it if I were you.
Check out my other post above for instructions and location again. Let me know if you need more help , no special soil required , just sun , water and food...sounds like me on vacation..lol..
Good luck Judith on whatever you decided !