Edited to correct myself:
No, you don’t—you can keep it on the master page. See Galen Shaffer’s and Wolff’s replies for details.
Original answer left here for posterity, giving an alternative approach that may perhaps be a better option in some limited circumstances:
Elements that are on a master page will always, by definition, be behind any elements defined (or overridden) on individual document pages. That's their very nature.
You don't mention exactly what type of document you're working on, or whether you have facing pages and the page with the image may switch from a left page to a right page.
If text reflow may cause the page to change from a left to a right page, then start with step 1 below; otherwise start with step 2.
Make sure that your company name on the master page is set up in a way so that it automatically positions itself correctly regardless of whether it appears on a right or left page. If the name is centred, this is not a problem—just make sure the text frame spans from the left margin to the right margin and center the text. If it is justified towards or away from the spine, make sure to use these options in the justification settings, rather than just left- or right-aligning them individually.
Copy the text frame with the company name, paste-in-place it (Cmd/Ctrl + Alt + Shift + V) on the page with the image (in front of it), and then anchor it to somewhere relevant in the text on the page so it's an anchored object.
Hide the image so you can see the company name behind it (to check that the added one is positioned correctly).
In the frame’s anchored object properties, specify where to place the object on the page. If you have facing pages, make sure the vertical offset is based on the page edge and the horizontal offset on the page margin; if you don't, both can be based on either, just as long as it gets the object into the right position, exactly on top of the one on the master page.
Unhide the image.
This should give you a duplicate company name in the exact same location as the one on the master page. If you're using facing spreads, it should also make sure that if the text reflows, this company name that sits on top of the image on the page will move with it and be placed correctly on the page, regardless of whether it ends up being a left page or a right page.