Improve MultiIndex label rename checks #24231

Job	Run time
Linux-Musl	15m 16s
Linux-32-bit	18m 32s
python-dev	0s
Pyodide build	24m 27s
windows-latest actions-310.yaml	37m 1s
windows-latest actions-311.yaml	33m 21s
windows-latest actions-313.yaml	40m 54s
windows-latest actions-312.yaml	35m 15s
macos-13 actions-310.yaml	32m 5s
macos-13 actions-313.yaml	30m 47s
macos-13 actions-311.yaml	25m 59s
macos-13 actions-312.yaml	26m 22s
macos-14 actions-312.yaml	21m 50s
macos-14 actions-311.yaml	21m 39s
macos-14 actions-310.yaml	25m 49s
macos-14 actions-313.yaml	21m 31s
ubuntu-24.04 actions-310.yaml	46m 17s
ubuntu-24.04 actions-313.yaml	48m 28s
Locale: zh_CN	22m 54s
Future infer strings (without pyarrow)	38m 49s
ubuntu-24.04 actions-312.yaml	43m 22s
ubuntu-24.04 actions-311.yaml	42m 8s
ubuntu-24.04-arm actions-313.yaml	35m 38s
Freethreading	21m 52s
Minimum Versions	23m 7s
Pypy	1m 24s
ubuntu-24.04-arm actions-310.yaml	35m 46s
ubuntu-24.04-arm actions-311.yaml	34m 42s
ubuntu-24.04-arm actions-312.yaml	36m 54s
Locale: it_IT	23m 55s
Numpy Dev	17m 10s
Pyarrow Nightly	19m 41s
Downstream Compat	5m 32s
Future infer strings	44m 34s
	15h 53m 1s

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