If a name was ever popular and then fell from popularity, then yes it can be dated, and it doesn't matter how old and/or classic it is. It's possible that
Katherine and all its variants will sound dated, if they fall in popularity enough.
I do think it's a tad boring due to centuries of overuse, yet it's not as boring to me as
Mary and
Jane are. It's like
Elizabeth that way.
I like
Kate and
Katie as nicknames.
In order of preference:
KatherineCatherineKathrynKatharine (I always want to take an eraser, rub that A out, and replace it with an E)