Looking for the name of this job scheduling algorithm
I don't know the name of the problem, but I do know the solution - this is the same problem that I had to solve for my algorithms course, just different terminology. The problem allows for a greedy choice. If you merely wanted a hint, then stop reading here because below is the solution. 

Greedy choice: you schedule the job with maximum profit on its deadline. (If jobs should be finished before the deadline, e.g. job 1 should be done before $t = 2$, then simply subtract one from the associated deadline.)

The algorithm is pretty much working backwards in deadlines, (starting at the latest deadline) scheduling the job with highest profit available on that deadline (this boils down to the greedy choice). 

I will leave the proof of the greedy choice as an exercise (read, I don't have a proper keyboard available, which isn't too great for my RSI, so I cannot write it now).