Lord of the Rainwood
Lord of the Rainwood is a title awarded to Davos Seaworth. It is not mentioned if this title makes Davos the liege lord of the noble houses established in the rainwood; for example, the Lord of the Marches is not the liege of all the marcher lords.
A Storm of Swords
When Stannis Baratheon names Ser Davos Seaworth as his new Hand, the king also grants the titles Lord of the Rainwood and Admiral of the Narrow Sea to the former smuggler. This promotes Davos from a mere landed knight to a high lord on par with the rest of the stormlords. Davos is proud his son Devan will one day be a lord.
Even now Davos could take great pleasure in the sight of his own blood keeping company with a princess and a king's bastard. Devan will be a lord now, not merely a knight. The Lord of the Rainwood. Davos took more pride in that than in wearing the title himself.—thoughts of Davos Seaworth