Animals and other objects lose their names after nametags being placed along with despawning. Renaming a rabbit "toast" will also lose its name and custom skin.
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Thank you for your report!
However, this issue is a duplicate of MCPE-26300. If you have additional information to add, please add it to that report.
Also, please remember to search to see if your issue has been reported previously. (Having similar problems on one report can really help us understand and resolve the problem sooner.) If you find a similar issue, you can upvote it and add your version, or if it's already closed as Fixed you can add a comment to request reopening it.

Mostly the despwning that happens to me is with named chickens and wolves(also tamed wolves).

Mostly the despwning that happens to me is with named chickens and wolves(also tamed wolves).
Thank you for your report!
However, this issue is a duplicate of MCPE-26300. If you have additional information to add, please add it to that report.
Also, please remember to search to see if your issue has been reported previously. (Having similar problems on one report can really help us understand and resolve the problem sooner.) If you find a similar issue, you can upvote it and add your version, or if it's already closed as Fixed you can add a comment to request reopening it.