They are quasi modal in that they express a similar idea, but that's all. Some people don't like the term modal to be applied so willy-nilly.
Your examples use present perfect.
Naomi hasaux hadlex to go.
They have aux hadlex to repeat the work.
Naomi has to go. Naomi had to go. Naomi has had to go.
They have to complete the work. They had to complete the work. They have had to complete the work.
The shades of meaning are the normal differences between the simple past and the present perfect. The present perfect implies that the speaker feels the past fact has some bearing upon or relevance to the present context, even if that connection is no more than the mere recency of the past event.
Let's say that a department manager met with her manager to discuss staffing needs. They decide to reduce the weekly hours of two employees because of reduced demand for their product or something like that. In a later meeting with the two employees, the manager, with her manager sitting beside her, might say:
We have had to reduce your hours.
They could say "We have to reduce your hours", casting it as a thing that is to happen. But in choosing to use the present perfect, they do two things: they acknowledge that the matter is at hand with the present, and with the perfect they present the decision as a fait accompli.
The employees are visibly upset when they leave the meeting. After they leave, the boss says to the manager:
We had to reduce their hours. There was no other choice, given the slump in our sales.
There, the decision is described with the simple past. It is over and done with.