It is possible to find ballasts for a specific brand of lamp - but not common. The most usual area you find that is actually with White SON lamps, particularly Iwasaki ones, which used a bespoke ballast for their lamps, providing it with an extremely carefully controlled waveform.
I don't think this is normally the case with MH lamps though. It's likely that you'll get the best performance/lifetime out of a lamp which is used with its respective ballast, but generally so long as the ratings and type of lamp are exactly the same, I'd expect it to work.
Ideal check: Go to the manufacturer's website for each lamp, and find the datasheets for them. If their operating characteristics are the same, you know that they should work right.
Only thing I can think of is if the new lamp's a quartz style MH lamp, as the old was a ceramic type (or vice-versa), I cannot remember, but I believe these may have had slightly different electrical characteristics (Go take a look at
Lamptech For more details there to prove or disprove my theory on that count!