That’s not true at all. Supports are very different from healers in MMORPGs especially. Supports are characters like Bards in MMOs who focus on boosting their teammates performance with buffs and debuffs to the enemy. The same is true in MOBAs, there’s usually a difference between supports vs healer characters
You will never catch someone calling a Holy Priest or Resto Druid in WoW a “support”. They are exclusively called healers. In fact WoW just added it’s first Support spec that buffs allies, and it even falls under the DPS category.
OW is called the Support role because while they all have healing, yes (albeit varying degrees of it), that is not what makes Supports unique or strong. You pick Ana for anti and sleep. You pick Zen for Discord and high damage output. You pick Mercy for damage boost and mobility. You pick Moira for strong heals and annoying flanker DPS pressure. You pick Lucio for speed and boops. And almost all of them have high damage/kill potential, which most “healers” in games do not
People who want to rename them Healer are usually just low ranked players with a poor understanding of Overwatch as a game