Improve MultiIndex label rename checks #24372

Job	Run time
Linux-Musl	15m 15s
python-dev	0s
Linux-32-bit	18m 34s
windows-latest actions-313.yaml	41m 49s
macos-13 actions-310.yaml	34m 39s
macos-13 actions-311.yaml	44m 38s
macos-14 actions-310.yaml	16m 55s
macos-13 actions-312.yaml	27m 29s
macos-14 actions-312.yaml	18m 33s
windows-latest actions-310.yaml	35m 37s
macos-13 actions-313.yaml	33m 15s
macos-14 actions-311.yaml	19m 48s
windows-latest actions-311.yaml	34m 0s
macos-14 actions-313.yaml	20m 24s
windows-latest actions-312.yaml	35m 6s
Pyodide build	23m 13s
ubuntu-24.04-arm actions-311.yaml	34m 3s
Pypy	1m 15s
Minimum Versions	23m 4s
Locale: it_IT	23m 31s
Numpy Dev	16m 37s
ubuntu-24.04 actions-311.yaml	42m 21s
ubuntu-24.04-arm actions-310.yaml	36m 55s
ubuntu-24.04-arm actions-312.yaml	35m 36s
ubuntu-24.04-arm actions-313.yaml	36m 28s
Future infer strings	45m 16s
Downstream Compat	5m 41s
Freethreading	21m 13s
ubuntu-24.04 actions-310.yaml	45m 24s
ubuntu-24.04 actions-312.yaml	43m 0s
ubuntu-24.04 actions-313.yaml	46m 21s
Future infer strings (without pyarrow)	39m 19s
Locale: zh_CN	23m 19s
Pyarrow Nightly	20m 19s
	15h 58m 57s

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