Overcalls at duplicate Bridge
There are two questions here:


(Terminology) Is making a bid over an opponent still called an overcall if your partner has already bid?


There are two competing uses (from Merriam-Webster):


  Definition of overcall
  
  transitive verb
  :  to make a higher bid than (the previous bid or bidder) in a card game
  
  intransitive verb
  :  to bid over an opponent's bid in bridge when one's partner has not bid or doubled


The first sounds a bit old fashioned, and the second is what I'd expect in modern bridge books, which tend to (cf. this lesson by Larry Cohen) use the names:

West, Partner (Opener): 1 Club

North, TD (Overcaller): 1 Spade

East, You (Responder): 2 Hearts

South (Advancer): [to call]


Did your partner need to alert your bid, regardless of terminology?


No, at least not in the American Contract Bridge League. See the Alert Procedures:


  Definition of expected length for natural bids for the Alert Procedure
  
  Suit bids:
  
  Three or more in a minor suit
  (Also: An opening bid of 1♣ is natural if, by agreement, it may be exactly
  4=4=3=2 with two clubs, three diamonds, and four cards in each major.)
  
   Four or more in a major for opening bids, rebids and responses
  
   Four or more for an overcall at the one level, five or more for higher levels
  
   Five or more for a weak two-bid
  
   Six or more for a weak three-bid


Side Note: It doesn't matter to the result, but I couldn't find the definition of overcall that the ACBL Alert Procedures are using. I would expect from experience that it is the second one.