There are at least two possible meanings of the name, probably more.
The word "halk" is Middle English and is actually used by Chaucer in The Canterbury Tales.It means "a nook or corner".The "-yard" part of the name possibly derives from Old English "geard" meaning a piece of land.Therefore the name might derive from a description of "the people who farm the land in the nook/corner".This is quite an attractive idea, but it's probably a bit fanciful.
The other possible derivation is more prosaic, but probably closer to the truth.The spelling of surnames did not become fixed until comparitively recently (18th/19th centuries). The modern use of the letter "W" was,in the past, often interchangeable with the letters "LK".For example, I've seen Halker and Hawker, Halksworth and Hawksworth and, of course, Halkyard and Hawkyard (I worked with someone called Tom Hawkyard a few years back).So, our name may simply be an archaic spelling of Hawkyard. But..................
I'm not an expert on phonetics, but it strikes me as strange that - in England at least - the "lk" part of the name is clearly pronounced.And the first "a" vowel in the name is pronounced as in "hawk".I doubt whether our ancestors would have suddenly started pronouncing the name in this way if, until they learned to read, they called themselves "Hawkyard" - which is quite different in pronunciation from the more complex "Halkyard".In fact, in Lancashire (where my branch hails from) the "H" is missing in pronunciation - so phonetically it sounded like "Aawlkyurd" when my grandfather Sam said his name.
If anyone has nay further thoughts on this, I'd be very interested to hear them.
best wishes to all the other members of our small clan,
PS - the Scottish connection is, I'm afraid, nonsense. As are any ideas that it's Scandinavian (I've had that one thrown at me countless times). This is most definitely an English surname.