Fix respawning of pool instances have different names #6096

Job	Run time
Local: Build & test on Ubuntu	30m 33s
Remote: Build & test (v23.1.0, false)	8m 57s
Build and smoke tests (ubuntu-latest, 3.8, false)	2m 42s
Remote: Build & test (v23.2.0, false)	11m 49s
Local: Build & test minimal package on Ubuntu	30m 25s
Build and smoke tests (ubuntu-latest, 3.9, false)	2m 37s
Remote: Build & test (v24.1.0, false)	8m 16s
Build and smoke tests (ubuntu-latest, 3.10, false)	2m 21s
Build and smoke tests (ubuntu-latest, 3.11, false)	2m 50s
Documentation style check	20s
Local: Build & test on Windows	0s
Build and smoke tests (windows-latest, 3.8, false)	3m 15s
Build and smoke tests (windows-latest, 3.9, false)	3m 6s
Build and smoke tests (windows-latest, 3.10, false)	4m 20s
Build and smoke tests (windows-latest, 3.11, false)	3m 53s
Build documentation	24m 12s
Upload dev documentation	0s
Deploy dev index docs	0s
Notify failed build	0s
release	1s
Upload release documentation	1s
Deploy stable docs index	1s
	2h 19m 39s

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