Yes, they are suckers and no, you don't need to remove them. That's the nature of Deutzia - its a caning shrub. Do you now what cultivar it is? Unless it is a dwarf variety a pot is not going to contain it for long.

It is a pretty young plant to tell for sure (and also not the clearest photo) but deutzias are considered a caning shrub - that is, they routinely produce new stems from the root crown, rather than just stems or branches off of a single trunk. I have seen older, mature non-dwarf forms of this shrub that can be quite massive - 6-8' across at the base.

So yes, if indeed a deutzia, the shoots/suckers are perfectly natural and do not need to be removed.

(LOL!! floral - I was writing as you were posting :-))

If you want more, you can divide off some of the suckers to form new bushes, just like with other caning shrubs.

Ahh that's good to know on all counts. It's a Strawberry Fields variety - I'd had one a few yrs ago which I stupidly gave away a year after it had produced the most glorious flowes as I was clearing out my yard of all my old plants which were diseased & it just got added in accidentally. However, my hopes this time round were to consider making it into a bonsai shrub as I'm not really able to manage large pots any longer, but if it's going to be as you say, perhaps a futile option??

They renew and continue themselves with new canes from the base so you specifically do not want to cut these off. Instead you occasionally cut out the oldest, twiggiest canes as these become apparent in winter.