In your case, the bioreplicate ID should represent a unique donor (for example, C1D1 for condition 1, donor 1). You do not need to add the technical replicate number (so not C1D1T1). If two runs have the same bioreplicate ID and condition, MSstats will automatically understand that they are technical replicates.
For more details and an example, you can look at Supplementary Table 1 in the MSstats v4 paper (link). See Supplementary Table 2 in case your experiment is a repeated measures / time-course design.
Posting a follow up question in case others have similar questions:
"If I have donor 1-5 across 2 conditions (each donor have two conditions), should I use "D1" instead of "C1D1", correct?"
My response: Here, I would use "D1" instead of "C1D1". Supplementary table 3 & supplementary figure 6 should be good references (link). This study can be treated like a paired design.