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I would think about what function that marching T or R is performing for the
user. It sounds to me like the character marching across the screen is
telling the user two things. First, it is reminding the user what is
happening; the user is transmitting data (or receiving data if it's an R).
Second, the marching character is reassuring the user that the system is
still functioning properly. Any time a system is tied up performing a task
for up to 45 minutes, there is a danger that the user will lose patience and
decide that the system is frozen or stuck in a loop of some kind.
If the user understands what the marching character means, that is, to me,
more important than the specific name you give it.