Some interesting possible origins of the Gardner surname:

Charles Wareing Bardsley gives the Gardner surname as part of the class of patronymics known as occupative - in other words, Gardners worked taking care of gardens.  It is also possible, however, that the name derives from two  Saxon words:  "gar" signifying a weapon dart, like a javelin, and "dyn"  indicating a sound, noise or alarm.  The "er" ending denotes habitation of a specific place.

A third derivation is from Bradleys dictionary of England and Welsh surnames, which indicates the name is derived from the Gaelic "Gairden", meaning (gair) an enclosed or fortified place, the beacon hill and (den) an outcry or alarm.  The Gairden-er, then was a warrior, one who bears arms, and is spelled today as Gardiner, Gardener or Gardner.

The name Gardiner appears in English Medieval registers, and the earliest recorded (1273) ones include the French masculine article, "le".  One of the earliest of the Gardiner names found are Geoffrey le Gardiner, of Oxfordshire; Ralph le Gardiner, of Huntingdonshire; and William le Gardiner, of Lincolnshire.

Several Gardiner-Gardner families in England have been granted armorial  bearings, some of the resembling each other in essential features, and others in  minor details.  Sir Osbern Gardiner, of Wigan Co., Lancashire, has a Coat  of Arms nearly identical to the one belonging to the Gardiner family of Newport,  Rhode Island.  There is a tradition that Sir Osbern (b. 1128) earned  the crest on his Coat of Arms in 1191 by chopping through the shoulder of a saracen who was about to kill Richard Couer de Lion. 

In the Americas, George Gardiner of Newport spelled his name with an "i", as  did most of his relatives who remained in Rhode Island.  Those of the  family who moved to Connecticut generall dropped the "i", possibly to distinguish  them from the Lion Gardiner family of Gardiner's Island, New York.

For information about the connection between New England Gardners and those across the Atlantic Ocean, check out this article.