Yes.
Red is the favorite color of the Chinese nation, and has even become the cultural totem and spiritual refuge of the Chinese people.
In ancient times, it was said that the name of a prisoner sentenced to death was written in red, so the description was unlucky. However, red also represents happiness. Whether it is daughters dressing up or literati performing ink, the Chinese people widely use red. So it’s totally fine to sign your initials in red pen.