What kind of server startup you mean when you are talking about a standalone server? Do you use mysqld_safe, or start mysqld binary directly?
I mean the conventional way to start/use MariaDB (with mysqld_safe , [mysqld] section in /etc/my.cnf and init control (/etc/init.d/mysql)).
Also, just checked MariaDB10, same behavior ;(
Thanks for the clarification.
So, there are several issues in here.
1. pidfile name does not use log-basename – it's a problem of the startup script (/etc/init.d/mysql), at least on RPM-based systems. At some point it checks if a path to the pid file is set explicitly, and if not, sets it to <hostname>.pid. It has no notion of log-basename.
2. no syslog if log-basename is given – it's a problem of mysqld_safe. It does have a notion of log-basename, and if it finds it among the options, it sets a value for the error log file name accordingly. But later it uses this variable to check whether the variable is set, assuming it was done by the user, and if it's not empty, the script claims that the user provided wrong configuration – set the error log name and requested syslog at the same time (the output of mysqld_safe says just that: "Can't log to error log and syslog at the same time..."
Since both bugs are outside the server, apparently mysqld_multi is not anyhow affected by them, hence it behaves correctly.
It's awful that historically there are so many steps in the process where the values are used and modified, it has always been a big welcome for all kinds of bugs.
3. The behavior with the empty error log – it's arguably acceptable, the expectations are vague here and might depend on the order of the given options. On one hand, when the value is empty, it's supposed to be set to <hostname>.err; on the other hand, log-basename is expected to modify the prefix. I wouldn't want any changes to be made for this special case unless you think it's certainly incorrect and have a good suggestion on how to make it consistent.
Hi Elena, you are right! I've reviewed it again and rechecked mysql init and mysqld_safe scripts.
While pid file can be explicitly mentioned in my.cnf (or a patch with my_print_defaults introduced) , the combination of both log-basename and syslog variables is a real show stopper.
I don't want to touch mysqld_safe for now as there could be some intentional logic to avoid conflicts that I am unaware about.
I am leaving it to MariaDB team to decide what's next 
We'll keep using all logs/pids explicitly defined in my.cnf for now because we use syslog everywhere, except for a few cases where we use mysqld_multi.
p.s. Maybe it's about time to consolidate mysqld_multi and mysqld_safe into something smarter, just to avoid fixing legacy bugs of both scripts
Thanks!
Alex