Unfortunately it looks like Google Assistant does not support this tag yet.
I also find this frustrating because my responses have a lot of names in them which are being read out incorrectly.
Currently the documentation for Google's SSML is defined here:
https://developers.google.com/actions/reference/ssml
See the following caveat on this page:
Note that not all of the elements and options described in the W3 SSML
specification are currently supported by the Actions on Google
platform. This page details which elements and options are available
for your application. The W3 reference links provided below may be
helpful for additional context and examples.
Unfortunately, there is no mention of "phoneme" support.
However Google does provide some additional features not in the standard SSML reference such as the tag (parallel audio responses).
One way you can work around this issue is to make use of the SUB tag.
You can substitute an alias phrase to replace the content inside the tag.
An example of pronouncing Daniel Ricciardo's name as he does:-
<speak>Daniel <sub alias=\"Rickardo\">Ricciardo</sub></speak>
See the following link for more information:
https://developer.amazon.com/docs/custom-skills/speech-synthesis-markup-language-ssml-reference.html#sub