mgmt: mcumgr: grp: os_mgmt: Fix issue and add xtensa

Fixes an issue with a missing else as part of a condition and adds
xtensa.

Signed-off-by: Jamie McCrae <jamie.mccrae@nordicsemi.no>
diff --git a/subsys/mgmt/mcumgr/grp/os_mgmt/include/os_mgmt_processor.h b/subsys/mgmt/mcumgr/grp/os_mgmt/include/os_mgmt_processor.h
index 60a6b94..3eebd3f 100644
--- a/subsys/mgmt/mcumgr/grp/os_mgmt/include/os_mgmt_processor.h
+++ b/subsys/mgmt/mcumgr/grp/os_mgmt/include/os_mgmt_processor.h
@@ -89,14 +89,13 @@
 #elif defined(CONFIG_ARM64)
 #if defined(CONFIG_CPU_CORTEX_A53)
 #define PROCESSOR_NAME "cortex-a53"
-#if defined(CONFIG_CPU_CORTEX_A55)
+#elif defined(CONFIG_CPU_CORTEX_A55)
 #define PROCESSOR_NAME "cortex-a55"
 #elif defined(CONFIG_CPU_CORTEX_A72)
 #define PROCESSOR_NAME "cortex-a72"
 #elif defined(CONFIG_CPU_CORTEX_R82)
 #define PROCESSOR_NAME "armv8.4-a+nolse"
 #endif
-#endif
 #elif defined(CONFIG_ARC)
 #if defined(CONFIG_CPU_EM4_FPUS)
 #define PROCESSOR_NAME "em4_fpus"
@@ -125,6 +124,8 @@
 #endif
 #elif defined(CONFIG_RISCV)
 #define PROCESSOR_NAME "riscv"
+#elif defined(CONFIG_XTENSA)
+#define PROCESSOR_NAME "xtensa"
 #endif
 
 #ifndef PROCESSOR_NAME