der Hahn
rooster
A male chicken known for its crowing.
Jeden Morgen weckt uns der Hahn vom Nachbarn.
Every morning, the neighbor's rooster wakes us up.

rooster / tap
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rooster
A male chicken known for its crowing.
Jeden Morgen weckt uns der Hahn vom Nachbarn.
Every morning, the neighbor's rooster wakes us up.

You can easily recognize the meaning of 'Hahn' from context. If people are talking about animals, a farm, or the verb 'krähen' (to crow), it refers to the male chicken. If the topic is water, the kitchen, or the bathroom, it means the water tap.
Auf dem Bauernhof krähte der Hahn schon früh am Morgen.
On the farm, the rooster crowed early in the morning.
For a water tap, the separable verbs 'aufdrehen' (to turn on) and 'zudrehen' (to turn off) are essential. The prefix appears at the end of the sentence.
Dreh bitte den Hahn auf, ich brauche heißes Wasser.
Please turn on the tap; I need hot water.
To make the meaning more precise, 'Hahn' is often used in compound words. The most common are 'der Wasserhahn' (water tap) and 'der Gashahn' (gas valve).
Der Installateur repariert den undichten Wasserhahn.
The plumber is repairing the leaky tap.
The characteristic sound that a rooster makes is described with the verb 'krähen' (to crow). This combination is very typical.
Jeden Morgen um fünf Uhr kräht der Hahn.
Every morning at five o'clock, the rooster crows.
The expression 'der Hahn im Korb sein' (to be the rooster in the basket / the only man among women) is a fixed idiom. It is always used in this form with the verb 'sein' (to be).
Als einziger Mann unter all seinen Kolleginnen war er der Hahn im Korb.
As the only man among all his female colleagues, he was the center of attention.
hammer
'der Hammer' and 'der Hahn' can both have to do with striking, but in very different areas. 'der Hammer' is a tool used, for example, to drive in nails. 'der Hahn' can be a part of a firearm that fires the shot. The words can be confused because both are short and, in some technical situations, have something to do with striking or triggering. In everyday language, 'Hammer' almost always means the tool, while 'Hahn' is much more often an animal or a water tap.

Der alte Hahn der Waffe klemmte, deshalb wurde sie nicht benutzt.
The old hammer of the gun was jammed, so it was not used.
Für den neuen Schrank braucht Max einen Hammer und ein paar Nägel.
For the new cabinet, Max needs a hammer and a few nails.