As follows:

It is ok to write your name in red pen, but try not to write your name in red pen. It is more formal to use a black signature pen. Although the red pen plays an irreplaceable role and significance for some needs, it will only be used in some specific occasions, such as teachers marking papers and doctors canceling medical orders.

The names of calligraphy works can't be written in red, but they can be replaced by seals. The seals are red, which can be accepted by people and play an embellishment role.

why try not to write your name in red ink?

There are two general reasons. First, in ancient times, whenever someone was sentenced to death, his name was written in chicken blood. The names of other prisoners must not be red, otherwise this mistake is not a trivial matter. If everyone knows this rule, normal people will definitely feel uncomfortable when their names are written in red.

The second reason is that emperors in many dynasties in history used red pen to read the memorial, and ordinary people naturally could not use the same color as the emperor, which is a taboo. The emperor must be unique.