How should you specify a diode?
If the diode is rated for 1A it can carry 1A of current under the conditions specified in the datsheet (and as long as you're not violating any of the other specs in the datasheet).
Most engineers in general will want to apply some derating criteria to components, so we don't use a 1A diode to carry 1A, we would pick a 2A diode for a 50% derating for example.
That applies to reverse voltage standoff, power dissipation, peak current, etc.
Your derating depends on your system design goals or specifications if you have them.