The trope is named for Giacomo Casanova(1725-1798), a soldier, spy, diplomat, adventurer, and librarian whose extensive but unreliable autobiography (in which he almost literally described himself as God's Gift to Women) established his eternal fame as a lover.
It should be noted that the historical Casanova was closer to a Chivalrous Pervert who really was looking for love...
See More Friends, More Benefits for when the mechanics of a game encourage the player character to act this way.
If the guy is actually only to be a Casanova and has no evidence onscreen, it's the Urban Legend Love Life.
If he develops feelings for one of his conquests (or someone who refuses him), he's a Ladykiller in Love.
The latter is considered one of the more faithful adaptations of Casanova's memoirs, while Fellini's... For the juvenile version — all of the above without the sex — see Kid-anova.
Contrast the Serial Romeo (who falls in love with a long succession of women, one at a time and for reasonable periods).
If they really get around but want to settle down, it's Looking for Love in All the Wrong Places.