BigR;
A-Sqare built the rifles and produced the ammo, and the SAAMI standardization data calls it the .338/06 A-Square.
Weatherby produced the Super BigGame Master MkV in the .338/06 but called it the .338/06 Weatherby, as well but no longer catalogs it except as a special order option. Ammo is still available in the Weatherby version (same cartridge, just different names).
Lee stamps it's dies .338/06 Ackley to keep from having to pay license fee's to the recievership for A-Square for use of the name.
You can very cheaply build yourself a .338/06 if you want one.
You can either get a Savage M110 or a Mauser M98 variant and order a barrel from MidwayUSA and have a gunsmith install the barrel, or even order the tools from MidwayUSA and build it yourself.
I bought my barrel on sale for $57.00. A gunsmith charged me $100.00 to fit, ream, and blue the barrel and action of my MkX Mauser. Throw in the dies that cast $22.00 and voila, in 3 weeks I had my custom .338/06.
It, with ammo it likes will shoot to about 1" for 3-shots, maybe better with the best load but Nosler no longer makes that bullet (180gr BallisticTip) though they do make the 180gr Accubond at 2x the price. I routinely see 2,900-3,000fps with a 180gr, 2,800fps with a 200gr, 2700+ with a 210-215, and 2,600+ with a 225. I've yet to run across a "deal" on some 250's so I haven't tried any yet. Its basically a ".300magnum" from a .30/06 case. It gets roughly the same velocity as the .338winmag with a bullet weighing ~20-25grs lighter.
I would suggest though that you go with the .35Whelen. There are more bullet options, especially the excellent 200gr Remington Corlokt PtdSpt. for general use, also more readily available factory ammo (Remington). Ballistic difference is nothing to make note of. Just a few higher digits on the chrono for the .338 than the .35.
Or, save yourself a bundle and stick with the .30/06 and 2-3boxes of factory ammo every year. (but what fun is that ??)