I have a differential signal up to 1.5 MHz and have to transform it to a single ended signal.
I have found this amplifier which has a BW of 2.2 MHz and should therefore be okay for this task.
The manufacturer also offers a simulation program, where I've tested this 
where \$R_f = R_g \$ and \$R_1 = R_2\$.
The input signals are 500mV pp and have a common voltage of 1V. Is this the right way of transforming a differential signal to a single-ended one?
It's one right way, assuming that the other characteristics of this circuit are acceptable in your application.
For example, the input impedance is relatively low, compared, say, to an instrumentation amplifier. But if your source impedance is low, it shouldn't be a problem.
It also requires careful resistor matching in order to achieve a high CMRR. But matched resistor networks are readily available, as well as amplifiers that have the resistors integrated right on the chip.
EDIT: My comments above were based solely on looking at the topology of the circuit diagram in your question. However, the amplifier you linked to, the AD8422, actually is an instrumentation amplifier, so that circuit diagram does not apply.
If the performance must be equal from 0 to 1.5MHz, I would try a high frequency differential amplifier IC, for example AD8132. Your current candidate has specs which seem to dive at much lower frequencies than 1.5MHz - for example the max output amplitude is virtually zero at 1MHz. High frequency differential amp ICs are fully usable to several tens of megahertzes, even higher.
