import re

def is_valid_variable_name(name: str) -> bool:
    # Check if the length of the name is within the allowed range
    if len(name) > 255:
        return False
    
    # Regular expression to match valid JavaScript variable names
    pattern = re.compile(r'^[a-zA-Z_$][a-zA-Z0-9_$]*$')
    
    # Match the name against the pattern
    return bool(pattern.match(name))