there is a conjecture for which I do not know how it is called. The conjecture is:
Every even number can be always written as the difference between two prime numbers.
Could you please help me to know how it is called?
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The specific conjecture that every even number is the difference of two primes appears to be due to Maillet (1905) as per the paper mentioned in comments.
However, I have never heard this name before. What is a quite common name, also mentioned in comments but perhaps somewhat misleadingly, for something related (but stronger) is de Polignac's conjecture stating that every even number is the difference of infinitely many pairs of consecutive primes. This conjecture is also older (1849), which might explain why the more recent weaker one is not so commonly known.
In addition, also from the mentioned paper, Kronecker (1901) made the conjecture that every even number is the difference of infinitely many pairs of primes (so stronger than Maillet but weaker than de Polignac).
Finally, a still stronger conjecture would be the (first) Hardy-Littlewood conjecture.