Yes, you can use a different brand charger for your cordless tool battery, but there are important considerations to ensure safety and compatibility. First, check the voltage and amperage ratings of both the battery and the charger. They must match to avoid overcharging or undercharging, which can damage the battery or reduce its lifespan. 
Next, ensure the charger is designed for the same battery chemistry (e.g., NiCd, NiMH, Li-ion) as your battery. Using a charger meant for a different chemistry can lead to improper charging and potential safety hazards. 
Additionally, verify the connector type. The charger must physically fit the battery's charging port. Some brands use proprietary connectors, so an adapter might be necessary if the connectors differ.
It's also advisable to check for any warranty implications. Using a non-original charger might void the warranty of your battery or tool. 
Finally, consider the reputation and quality of the alternative charger. Opt for chargers from reputable manufacturers to ensure they have the necessary safety features, such as overcharge protection, short circuit protection, and temperature control.
In summary, while using a different brand charger is possible, it requires careful attention to voltage, amperage, battery chemistry, connector compatibility, and safety features to ensure proper and safe charging.