The word that describes maintaining your body on the water surface

You are looking for (to) float:

• to stay on the surface of a liquid and not sink:
  • An empty bottle will float. You can float very easily in/on the Dead Sea because it's so salty.

(Cambridge Dictionary)

To flounder might be a suitable word.

From Google:

Flounder struggle or stagger clumsily in mud or water. "he was floundering about in the shallow offshore waters".

(To do it successfully would probably be treading water).

When desperate, an individual has been said to "thrash the water to foam."

Less desperation will allow one with some presence of mind to flail, flounder, founder, and possibly fail in a struggle to survive drowning and suffocation.

The Wikipedia article on treading water has some terms for this, and whilst some imply person in the water can swim, dog paddle implies poor if any swimming ability.

More experienced swimmers often find their own method of staying above the surface. These techniques often involve sculling, flutter kick, and other unofficial techniques of staying above the surface. [...]
The eggbeater kick is a highly refined and efficient method [...].
The dog paddle is a simple style often used instinctively by children. It involves waving both hands & legs randomly while "on all fours".

And another dog paddle definition from O-D

An elementary swimming stroke in which the swimmer beats at the water with the hands in a manner resembling a swimming dog