One general sense I get from Iranian historiography is that Iran under the Ikhanate and Timurid dynasties are not really considered Iran in the 'proper' sense.
However it occurs to me that the distinction seems artificial: both states were founded by non Iranian conquerers who eventually adopted the local language and culture. If this sounds at all familiar, this is the same story as the Safavid dynasty.
So in contemporary times, were the Timurids and Ikhanates considered kings of Iran, and was the state they ruled considered by outsiders to be Iranian?
Yes, more can be said, but I go into some of the consequences of the Ilkhanate for Iranian identity here: https://www.reddit.com/r/AskHistorians/comments/96kevr/did_genghis_khan_leave_any_religious_or/e41x3kv?utm_source=reddit-android
The Ilkhan Ghazan was arguably the first to conceive himself as "Padishah of Iran" in the modern sense, where "Iran" refers to a geographical region, not (as in Middle Persian) an ethno-religious group. That said, the Safavids were responsible for the prominence of Shi'a Islam, which came to be a defining aspect of Iran.
I have deliberately ignored arguments over whether Timur or Isma'il or some other ruler were "Persianized" enough for one standard or another, as IMO they only invite anachronism.
ETA: As for the way outsiders viewed it, it depends on what outsiders you mean, and in any case they didn't have a conception of "Iran" like we do today. The region would most commonly have been known as "Persia" or "Ajam" (The latter meaning roughly "land of the mumblers" [i.e. "those whose speech cannot be understood"] in Arabic).