What is the correct gain of an RRC Filter?
The gain is completely arbitrary and you can scale it as desired for the overall receiver or transmitter design. Where special attention must be paid is with fixed point design where the best practice is to let the filters grow the signal- do not scale the coefficients or the input as that only introduces more quantization noise and degrades SNR. Let the filter grow (extended precision accumulators!) and then scale the output as you would do for any gain adjust to bring the signal level to within the range of the precision used.
Typical design practice for fixed point design which avoids precision errors is to use 2 more bits of quantization for the coefficients, sum the weighted taps in an extended precision accumulator and then scale the output to any level desired. In this case the quantization of the coefficients (if the same or less than the datapath) would cause the implementation to not meet the expected rejection and passband ripple given by the floating point equivalent design. Typically we want rejection to be greater than the quantization noise floor, and a reasonable rule-of-thumb is that the achievable rejection will be 5-6 dB/bit of coefficient quantization.
I detail this further at this post showing the quantization error contributions (such that you can also see if you want to limit the accumulator precision that you can scale after so many taps since the trade between quantization noise and accumulator precision is clearer, but in general the safest/easiest approach without further computation is to just wait until the out and let the accumulator be $log_2(N)+2$ higher in precision than the datapath where N is the number of taps in the filter.
Inter-filter bit width
This is further detailed here within the context of a general approach to FIR filter design:
what is the suitable design Method to the filter?
The graphics below demonstrate the quantization effects on a typical low pass FIR filter. This motivates the &quot;best-practice&quot; to use 2 more bits of quantization for the coefficients over what is used in the datapath, and the noise summation process in the filter motivates using extended precision accumulators and let the filter grow the signal (then truncate at the end) as detailed in the links above: