score:8
If anything, it would be the other way around.
Boaz was David's great grandfather. Solomon was David's son.
The Temple wasn't built until Solomon's time.
According to Eerdmann's Dictionary of the Bible, some scholars believe the names of the columns may have gotten their names from "a dynastic inscription" upon them. Since Boaz is, indeed, in David's lineage, it is entirely possible that the column was named after Ruth's kinsman redeemer, the forefather of the great king.
(That was pretty cool, by the way, hadn't noted the connection before. Thanks!)
Upvote:6
As neither the Bible nor any other source that I know of says where Solomon got these names, we can only speculate.
It's possible he named Boaz after his ancestor. Note he named the other pillar Jachin. The only mention I can find of a Jachin in the Bible before Solomon's time is Gen 46:10 and some related passages where it says that one of Simeon's sons was named Jachin. This would not have been an ancestor of Solomon. As nothing else is said about him, I'm inclined to think he wasn't particularly famous, though of course it's possible that he was famous in Solomon's day but accounts of him are now lost.
Note that in Hebrew, Boaz means "strength" and Jachin "establishment" or "certainty". It's possible that Solomon named the pillars with these meanings in mind, and not thinking of famous ancestors.
Or there may be some different reason entirely that is lost to us.