In 2001 Sally Tennant posted an item on Genealogy.com:

   The Tennant name is believed to come from Old French- 'Owner of a Tenement'
   Tennant ancestors can be traced back to ancient territories (between 11th & 12th century)
   of the Scotland England Border Ridings-Strathclyde Briton. 
   
   The name first appeared in records in Linlithgowshire (before 1100). Here,they held land
   and estates and were actively allied with other influential families.
   
   The Tennant family is distinguished as a clan {in those days, a family could only qualify 
   for clan status if they could prove their ability to put 250 armed men on horseback within
   1 hour to defend their clan, lands and properties. 
   
My Notes (1) Linlithgowshire stretched from Cramond near Edinburgh to the River Avon just west
            of todays town of Linlithgow and included South Queensferry.
         (2) Attempts to contact Sally for her source, failed.
         (3) Another suggestion is that Tenant is from the Latin "to hold"
         (4) See Ragman Rolls on my Scottish pages
                
In 2002 Paul Tennant posted an item on Genealogy.com:
   In reply to "What does our name mean?".  My sister researched (Writes Paul) the name
   and it goes as far back as the Romans.  When they colonised northern England, some troops 
   and Roman civilians went into "rented accommodation" and the owners of the properties were
   called Tenants.  They were also the earliest recorded defraudsters of "building insurers"
   because they burned them down when the Romans moved on.
	
My Notes (1) The county of Linlithgowshire is the location of the eastern end of the Antonine wall
   	a Roman earth and timber wall built as a boundary of the Roman empire 20 years after Hadrians wall,
   	The more well known Hadrians wall was a more substantial affair built some 100 miles 
  	further south, nearer todays border. As the Scots were the "enemy" the rented
   	accommodation would presumably be on the south side of the border making our origins at
   	at that time English, even if only temporarily until the border moved south! 
		
         (2)Cramond was the site of a Roman fort.
		

In 2003 Patricia Smith posted the following on Genealogy.com:
    The scottish surname Tennant is of occupational origin, being one of those surnames based on the name
    of the trade or profession once pursued by the original bearer.  In this sense the derivation from 
    the old French word tenant meaning a tenant of a house or rooms, holder of a tenement pertains.
    
    An early record of this name occurs in the concilia in 1309 - one Thomas Tenaunt is recorded therein
    in that year.  One John Tennant is listed as being one of the garrison of Edinburgh Castle in 1339 
    and one Andro Tennant is listed as being a Burgess of the region of Stirling in 1336.
    
    Notable bearers of this name include Smithson Tennant (1761-1815) an english chemist who made some 
    interesting discoveries as to the burning of metals. Variants of the name include Tenant and Tennent,
    my family who came from Airdrie and surrounds spell it all ways.
    
    The Blazon of Arms is:Argent a boar's head couped in chief and two crescents in base, all within a 
    bordure sable.  Translation: Argent (white) signifies Peace and Sincereity.  Sable (Black) denotes 
    Constancy. Crest: A sail proper.  Motto: Plena habit Deus V*** (God will fill our sails) and origin
    is Scotland.  

	
Link to the information on my Scottish Origins page