There is no written history to be offered or studied on the adoption of these names, as they predate Germanic literacy. But as to whether they were ever objected to, in the English Christian tradition? Not from leaders of the English Church during the period when the morpheme "Tiw" or "Woden" or "Thunor" or "Frige" had any popular association with a persona at all, so far as I know. Though for two of those, there is little to no period in which such protestations could have occurred and been recorded in any case, given the dearth of any direct reference to or description of Tiw or Frige in the Old English corpus. The absence of textual evidence for them or their hypothetical cults in Anglo-Saxon England simply makes it difficult to imagine a scenario where they are perceived as pagan cultural touchstones by the church or its advocates. For other reasons, I cannot see Woden or Thunor being perceived in this manner, but I will get to that in a bit.

What you have to understand is that subsequent to the conclusion of the Christianisation of the English kingdoms (the last of which, the Isle of Wight, in 686), there was little demonstrable sense of the remnant cultural leavings of the Germanic heroic/mythological/literary traditions being affronts to Christendom.

And indeed, there was quite a bit of syncretisation of traditions, in which context hagiographies and even biblical texts adopt the flavour and tropes of Germanic heroic poetry (e.g., the Old English Book of Judith). Or in which, for example, names for beings of Germanic lore can inject themselves into the language of Christian narrative, wrapped into a larger Germanic heroic narrative, in lines 111-114 of Beowulf, where we are told that

þanon untydras ealle onwocon,
eotenas ond ylfe ond orcneas,
swylce gigantas, þa wið gode wunnon
lange þrage; he him ðæs lean forgeald.

That is, that God contended with and repaid duly Elves and Orcs and Monsters and Giants (implicitly, as children of Cain). There is simply no sense of separate "pagan" and "Christian" conceptual spheres in the cultural mythology of the era.

And we don't find, therefore, for the most part, any objection (one to be discussed later) to those characters and ideas from prior storytelling and lore, as characters in inherent conflict with Christian ideas or values.

But as to "Thunor" and Thursday, the principal source of cultural currency for the name "Thunor", as of the 8th century (i.e., literate, Christian England), is really just the climatological phenomenon of thunder. The name is precisely the Old English word for thunder (and "thunres" being the genitive). And it is also attested as a contemporaneous personal name. To an Old English speaker, "Þunresdæg" is first and foremost "thunder's day". So a day's being named after it is not inherently to be interpreted as a day's being named after a pagan god.

Moreover, and in particular with respect to "Woden", the Anglo-Saxons had a strong penchant for euhemerism, which lent characters receiving this treatment another source of cultural currency which identified them as something other than Gods. So by in the 9th century, Woden is no longer a pagan god, but rather a heroic ancestor to the English kings, in the royal genealogies. And it is more contemporaneously accurate to regard this as the association to be made with the day (i.e., "Wodnesdæg"), therefore, during the Anglo-Saxon Christian era.

One very important and off-cited exception to this general trend of syncretisation is the letter of Alcuin to Hygebald, circa 797. Herein, Alcuin famously asks, of the English penchant for the maintenance of the heroic tradition even among the clergy, "What has [the Germanic hero] Ingeld to do with Christ?" Which is to say, why are monks writing of the heroic deeds of pagan ancestor figures, when they ought be writing of the word of God?

I'm hesitant to make too much of this, though. Through it, we can attest that such objections did exist. But not that they were overwhelmingly influential. As the need for Alcuin to object so strongly in the first place suggests that he was not getting his way as he saw it, in this regard.