Which is the correct preposition to use with rename?
- rename to
- rename as
- rename by
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You can have "Renamed A to B" (most common), "Renamed A as B" (less common) and "Renamed A, B". This last is not common, but is found in other related forms because "A was renamed to B" and "A was renamed B" or "A will be renamed to B" and "A will be renamed B" are all found.
By here would refer to how something was renamed. "A changed his name to B by deed-poll", "Renamed A to B by the
mv command", and so on.
Rename is derived from name, used as a verb. When one names something, one gives a name to a previously unnamed thing; when one renames something, one gives a new name to a thing that already has a name (which is to be discarded in the act of renaming). Because of that obvious connection, it is to be expected that rename will behave syntactically the same way as name (when used in the relevant way). And indeed it does. Consider:
The ship was named France. Later on, it was renamed Norway.
The two sentence seem perfectly natural. One doesn't feel that anything is missing after renamed in the second sentence, just as one doesn't feel that anything is missing after named in the first one. So the answer to the question is that in ordinary English rename is used without any of the prepositions offered by the OP.
It is true that name is sometimes used with as, as in
John Smith was named as a potential candidate for the position.
When so used, name is, however, used in the sense of identify by name rather than give a name (and it is the latter that is relevant here).
When by is used with name it is to introduce a term for somebody who performed the act of naming, rather than the name itself. By can be used with rename in the same way, but it does not seem that this is what the OP is asking about.
The people who use to with rename are probably guided by the fact that rename means the same as change the name; they use the preposition that would indeed be required for if one used the latter phrase. This usage is widespread enough that it can't be dismissed as incorrect, but it is seen mostly when rename stands for a software function. It can thus be regarded as a part of the computing-related jargon, rather than of ordinary English.