How Best to Rank for Multiple Keywords?? eCommerce site

I need to get some help here please ... having read lots in here about keywords, keyword density and anchor text I am trying to implement what I think now is good practice (not over optimizing) however I am becoming confused (and so is Google). I want to rank for more than one keyword / phrase out of necessity - users and google call the same product by different names which appear in different searches under different search terms and often the alternative names are not shown in 'related searches' indicating google doesn't see the relevance to the other names. So optimally ranking for one search term seems to adversely affect ranking for another term.

So how does one 'spread' effectively the use of keywords and anchor text in product description text, articles and other content on the site etc and primarily in internal links (where anchor text can be totally controlled) and external links that I may have control over.??

Would something including text like ... 'primary search term' is alternatively known also as 'other search term 1' and 'other search term 2' (and so on) somewhere on each product page and in site content in general, withany anchor text links back to home page being only the primary search term .... i.e. would google see enough of the other terms to assimilate the items to each other.?

cheers

For E-comm Site Research your keyword search volume if users are searching for with the product name keep the anchor link with same name and if you want to rank for some another keyword for same topics increase the density of keyword in your product description in this way you can rank with other keywords too.

Create a combination of your keywords you want to rank and add them in your description as well as title of your product try A/B testing with your keywords.